I had a lot of the same issues, being a single father with a demanding job for many years.

Work Out A Sustainable Cadence

Weekly may not be possible in the end. Figure out how frequently you can realistically attend, and ideally how to make that a regular schedule not random (because it's harder for people to accommodate random). Ways to up this:

1. You need to have a discussion with your wife and say you need regular time for a hobby. Negotiate what this could look like. Maybe you need to swap off "off periods" so you both can have a hobby, or pay for a babysitter and so it's also Mom's afternoon off, money allowing. When I was single dad of a very young child in a new city with no social support I could swing paying for a Sunday afternoon of babysitting every other week, so my cadence I could play was every other week.

2. It's hazy what is preventing you specifically from attending - what does "wife is unsupportive" mean especificamente to the situation? You need to break it down to the tangible issues. Is it that she wants to leave during that time and you're on child care duty? Or she "just wants you at home" for ineffable SO reasons? Then see if attending remotely is an option. My group had a member move away but he calls in via Google Hangout for a game every other week. Maybe your group isn't up for this, but that part comes next. You have to first clearly understand what your blockers are, and figure out what options you have. If it's "your wife expects you to participate in randomly planned events," then you can negotiate timing of those events or figure out if weeknights are better than weekends for you for gaming or whatever...

Come up with options of o que você pode fazer.

Find Out If Your Group Can Accommodate, Or Find One That Can, Or Found One That Can

Now that you know what you might be able to do, talk to your group and see if they are cool with that. If you can't attend weekly but can do biweekly, maybe they'd be open to alternating weekly campaigns (my gaming group does this for that reason, not everyone can do every week but some can, so we run 2 campaigns and some opt in for one, some for the other, and some for both as their lives allow).

See if attending remote is an option, and so on.

If there's not really a way to work it out with the current group and campaign, see if maybe there could be another campaign with some of your current group, or maybe even a totally new group. I know my gaming group has a lot of "spinoff" groups - this guy runs a game for a bunch of other people Friday night, these two are in a game with someone else - it doesn't have to be "These six people in this one campaign".

In fact, if you can't commit to a cadence, maybe more one-shot or pick-up gaming is what you are going to have to do.

Obviously all this is dependent on the other thing you need to break down and figure out, which is o que você quer. Where's your joy coming from? Gaming in general? This group in particular? D&D? Campaign play vs. one-shot play? Rank your desires. If there was a totally different group willing to meet whenever is good for you, is that your next-most-optimal scenario? Again, clarity is your friend here. Once you have that, then the group (existing and others) can also decide what they can do, and you fit your needs and their needs together.

Stay Plugged In Even If You Can't Attend

The answer may end up being "I want this group and I can't work out attending too much more and so this is my life now." But there's things you can do to participate somewhat even if you're not present.

First, if anyone's willing to write up session summaries, you can follow along that way. My group is in the habit of doing pretty long session writeups and we publish them on my blog, some are even like 12-page pdf types. This is fun and one of the corollaries is you can read them a bit as if you were there. This obviously requires someone to be willing to do this (though you can do it when you attend).

Second, even if they're not up for you attending remotely, maybe you could still listen in remotely. Via recording or even just via "hey put someone's cell phone on speaker and set it in the middle of the table and I'll listen on airpods as I do my honey-do list." A live podcast of your own game! I haven't done this for gaming but do it for work meetings all the time. "Here, watch on your own time."

If they are running your PC as a NPC while you're gone, you could ask them to text you from time to time with critical decisions or looking for pull quotes. Or just tell the DM ahead of time things you'd like him to say or do, so you can keep some things going in your absence.

Anyway, best of luck, you will probably have to give something to get something as part of these negotiations and tradeoffs, but if you can be crystal clear about what the hurdles are and what things you can/are willing to do, usually finding a solution isn't that hard.

In a similar situation, my group decided on having an alternate campaign

When I first started playing D&D locally, our group had 5 players plus the DM. At times, one player or another couldn't make it, but we still wanted to play. The primary main campaign really couldn't move forward without someone, so we just created a second alternate campaign where folks could drop in/out and would be scheduled on the weeks where someone couldn't make it. To make things slightly more complicated, this campaign was also done via rotating DM so that those who wanted to try DMing could. Each 'arc' would last anywhere from 1-4 sessions typically.

As you noted, this did create an issue of resources where someone who hadn't played had more resources than others. At times, the current DM would say what resources they had available (including HP/spell slots, etc.) and others they'd just let them come in at full strength. It was always up to the DM and no player ever had an issue with the ruling.

This system also meant there were XP/level differences. Sometimes as much as a 4 level differential. Amazingly, that never really seemed to be an issue or make one character more underpowered than others.

We never really encountered any issues with this and it gave us all an opportunity to play more D&D.

This may help solve the scheduling, but not your personal issue

While an alternative campaign helps resolve availability, it ignores the larger issue of lack of support at home for doing this. As with all things, commmunication is key.

I've got two kids and started playing right around when they were born. My wife was less than enthused, but having time away is just as healthy as time there. Talk with your wife, work out time for you to do this, and she should have time/the freedom to do things she likes to do. If those things are with you, that's great - but give her a chance to have a life outside as well. My wife and I communicate a lot and a big part of compromise is each giving each other space.

Things which I’ve seen suggested for similar situations:

1. Offer to host a session on a week that you can’t leave the family. Obviously, this will depend on whether your family will tolerate that, and whether your group will tolerate occasional interruptions by the family during the session. It does offer an opportunity to expose your family to your hobby, and perhaps encourage them to get involved in it (though not necessarily with this campaign).

   To the extent that your campaign group is willing to be flexible, this is probably the best solution, as it is the least disruptive to the campaign; the downside is that your spouse has indicated non-support, and hosting may be perceived as “stepping up” a potentially hostile situation (“I told you I didn’t like you going out to play those childish games every week, so you think that bringing them here is better?”).

2. If you, your DM, and/or the host of the session are equipped for it, participate via Skype or some other video conferencing software. Again, family tolerance is an issue here, as is group/DM tolerance for interruptions. It’s less of an opportunity for family integration, but the opportunity still exists - and will be somewhat less obtrusive for the group.

   This can work well, if all parties involved - which in your case, includes your spouse - are willing to tolerate it, and if the campaign group is willing to go through a bit of extra effort to set it up. Obviously, both you and the host are going to need the relevant software and hardware, including cameras, and some agreement will need to be arrived at for rolling dice. When I did this at a con, we handled rolling dice by making sure that both camera views included enough flat surface to roll dice on, and any non-hidden rolls were made to land in those areas - but some other alternatives I’ve seen proposed include another member of the group rolling for you by proxy, or using an on-line roller, such as a chatbot in an IRC session. I’ve seen mixed reviews for all of the above; my only direct experience has been with cameras showing the ‘roll zone’.

3. If your group and DM are willing to make a principal concession to your limitations, perhaps parallel campaigns would be the answer - that is, the campaign in which you are a character is run only when you’re available; on your “off” weeks, the rest of the group runs a different campaign, in which you aren’t a character. I tend not to like this one, as the less-frequently-run campaign tends to die sooner, and there’s always an air of exclusion associated with the other campaign.

   To the extent that your campaign group is willing to do this, it can work well - but not indefinitely. I’ve not participated in this sort of situation, but I tem heard of similar, and more often than not, the campaign that was played less often had a tendency to die, and the player that was absent from the other often ended up dropping out completely, including exiting the hobby entirely. This one really takes a bit of effort to maintain and keep inclusive, and is probably the least satisfactory of the ideas presented here.

Family is Important

Your family is important. You say:

I'm the only one who has kids, and unfortunately for me my wife is not exactly supportive either.

How old are the children? The "either" makes it sound like the children aren't supportive either. So, how much have you done to include or at least introduce your family in your hobby?

I personally introduced my wife and daughter to the game. In order to first capture my daughter's interest we used LEGO minifigs as the minis. We play spuratically, not every week or month, and so we just play when we have time. My wife started out rather uninterested in the game, and as we've played she has grown more and more interested in the stories we're telling and oft is the one that says "we've not played in while..."

Introducing them to the game and maybe running a game for them might get them to understand why you like it. That might allow them to allow you to spend more time in your current game.

Quid Quo Pro

If your wife is giving you one night a week to game, you need to reciprocate giving her another night of the week off to do her interests/hobbies. Are there other hobbies that take you away from the family? Do you oft travel for work? These things each could take their toll on family dynamics. Remember that relationships are bit like a bank account, you need to make deposits before you can make withdrawals. Always try to keep a positive balance with your wife and children.

Staying Connected to the Game

If you really aren't able to get your family life to release you every week with all the above. Work out with the DM and other players a story reason on why character disappears, so the gaps make sense in the narrative. Maybe someone cursed your characer to jump planes on random interval (like an odd form of blink), or you are spending a lot of time researching things in library on another plane, etc. Then when you can't make it, you can create a narrative about what you did in the other plane while banished or researching or whatever.

A very visible version of this is Ashley Johnson on Critical Role working across the country on the hit show Blind Spot. She would only be able to Skype in to play on occasion during a section of the first campaign. The DM worked with her to create the story that she physically at a temple of her character's god helping to restore it and gain worshipers, and that god was granting her an avatar to help her friends out at their time of need. At times when she couldn't make it, the DM would say that the avatar had faded. When she returned from filming, and the party stopped by the temple, it was revealed that the temple had been repaired, and she had gained followers including someone with enough knowledge and favor to "lead the flock". Allowing the character (and player) to pickup again.

We had one guy in this circumstance, I got a webcam so that he could continue to join in. Alternatively, if it's not too often, have someone knowledgeble on your character play it alongside their own. Our wizards big gun is conjure animals, if all I do for an absent wizard is conjure animals, it's a good use of their character. :)