Como o dano bônus do bárbaro causado pelo Rage interage com o combate com duas armas?

Two-handed weapons are not useless: bonus action and TWF

The two weapon fighting that a barbarian can use is not the same as the Fighter/Ranger fighting style option "Two-Weapon Fighting." Only that class feature allows the Fighter/Ranger to add their Ability Score Modifier to the second weapon's damage.

Each successful attack (using Strength) gets the Raiva bônus de dano

Assume a barbarian with a Strength of 16. (+3 damage modifier)

O Luta com duas armas rule (Chapter 9) states:

When you take the Attack action and attack with a light melee weapon that you’re holding in one hand, you can use a bonus action to attack with a different light melee weapon that you’re holding in the other hand. You don’t add your ability modifier to the damage of the bonus attack, unless that modifier is negative.

The Barbarian has to use a bonus action to trigger their Raiva (PHB, Chapter 3):

In battle, you fight with primal ferocity. On your turn, you can enter a rage as a bonus action. {snip} When you make a melee weapon attack using Strength, you gain a bonus to the damage roll that increases as you gain levels as a barbarian, as shown in the Rage Damage column of the Barbarian table.

Let's see how a three round battle will go.

1. Round 1, trigger rage and one 2H weapon attack, or, one hand axe attack plus rage.
2. Round 2. One attack with 2H weapon, two attacks with two weapons, STR bonus damage on only one
3. Round 3, One attack with 2H weapon, two attacks with two weapons, STR bonus damage on only one

Damage comparison

Two-handed sword versus two hand axes: damage if we presume that all attacks hit

1. Round 1: 2d6 + rage + STR (2d6+5) versus 1d6 + rage Str mod. (1d6+5)
   Advantage 2H weapon.

2. Round 2: 2d6 + rage + Str (2d6+5) versus 1d6 + 1d6 + rage + rage + str mod (only on first blow) (2d6 +7)
   Total after two rounds is: WH 4d6 + 6 + 4 (24) vs 3d6 + 6 + 6 (22.5) Slight lead to 2H weapon

3. Round 3: Same as round two, but now TWF takes a slight lead, since:

   All told, we see 6d6 + 15 from the 2H weapon. (Average 36)
   All told, we see 5d6 + 19 from the TWF choice. (Average 36.5)

Note: you gotta hit it to damage it.

An advantage accrues to the TWF approach if the fight lasts that long due to having more chances to hit. There are two chances to hit on the second and third rounds, whereas with the 2H weapon, there is only one chance to hit on each turn. You'll have a total of 5 attack rolls, rather than 3 attack rolls, if the dwarf goes with the two hand axes.

Com aquilo em mente, DerekStucki did an analysis of the choices confronting the Barbarian and suggested carrying both a Two Handed Weapon and two light one handed weapons. Why? Because the conditions of combat vary.

For what it's worth...

If the Barbarian takes the Dual Wielder Feat at level 4, they can use 1d8 damage dealing warhammers, battle axes, or long swords. The longer the battle goes on, the more two weapon fighting approach looks to be more advantageous. But, after level 5 where the Barbarian gets two attacks, this changes things enough that you may see the 2H weapon being a good or better choice.

• We have a number of Q&As that compare TWF with 2H-weapons that go into far more detail about that. Since you are dealing with a beginner that's not germane for this question. If she gets to level 4 and considers that feat, I suggest you drop a question here to ask about the pros and cons of the Dual Wielder Feat for a Barbarian versus fighting with two-handed weapons (and the related analysis of whether Great Weapon Fighting would be a a feat worth taking).

  The same three round fight with the dual wielder feat, at level 4, using battle axes (1d8) as one handed weapons, yields this result after three rounds

  All told, we see 6d6 + 15 from the 2H weapon. (Average 36)
  All told, we see 5d8 + 19 from the TWF choice. (Average 41.5) Round 1 is still "advantage 2H weapon" and round 2 is roughly a tie.

  This looks to be a little more attractive, except during the first round, and the 5 versus 3 attack rolls means that there will be fewer misses. Each miss by the 2H weapon is a bigger loss of damage to the target.

Things change at 5th level for most martial characters

The 2H weapon barbarian gets another spike in attractiveness no nível 5, so early rounds tend to favor the two handed weapon.

The Two-Handed Weapon Barbarian gets two attacks. TWF gets three on rounds 2 and subsequent, using the bonus action. Damage summary:

Round 1: 4d6+2Str+2Rage 2H vs 2d8+ 2Str + 2Rage for TWF Round 2: 4d6+2STR+2Rage vs 3d8+ 2Str + 3Rage (All subsequent rounds are per Round )

The fight has to go on for a bit longer than two rounds for the TWF to begin to show advantages.

If the Dwarf does not take a feat, but instead boosts Strength to 18 at level 4, all attacks hit more often, all attacks get another damage point boost from strength, and the 2H weapon approach begins to look more attractive.

The rage bonus is added to all your melee weapon attacks that use Strength

However, normally your only add your ability modifier to the damage from your main weapon attacks.

So, as you say, the attack with a greataxe (or any single weapon) would be:

Weapon damage die + Strength modifier

If you are raging then you add your rage bonus, so the full damage would be:

Weapon damage die + Strength modifier + Rage bonus.

Luta com duas armas

Veja as regras aqui. Citar:

When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand. You don't add your ability modifier to the damage of the bonus attack, unless that modifier is negative.

The emphasis is mine. So if you qualify for two weapon fighting (using light melee weapons), then your bônus attack with your second weapon would just be:

Weapon damage die + rage bonus (no strength mod)

Note that there is a 'fighting style' - an option for fighters and some other classes - that allow you to add your modifier to the damage of your bonus attack. But this is not accessible to a (single-classed) barbarian.

Para resumir:

Two-weapon fighting vs single weapon fighting is a trade off (Resposta de KorvinStarmast has a more detailed breakdown). Higher damage with a single weapon vs more lower-damage attacks with two weapons, and damage output can depend on your feats and the opponent's you are fighting.

Ultimately, I don't think the damage variance is that much to worry about, and I would go with whatever you think makes your character cooler!