George RR Martin já foi perguntado isso antes e esta foi sua resposta:
And lastly, why didn't Lord Tywin ever remarry after his wife died? Surely he would have had ample opportunities to do so? Thanks.
Maybe he didn't want to.
Westeros, So Spake Martin, POVs and the Red Viper
Quanto ao que podemos reunir do texto para comprovar isso, veja abaixo.
Existem algumas razões aqui, mas acredito que tudo se resume principalmente ao fato de que seu amor por sua esposa era tão profundo que ele não queria se casar novamente. É claro que ele já tinha herdeiros que naquele momento não estavam indo a lugar algum e herdariam a rocha. Por fim, ele pode não querer criar duas "facções rivais" em seus filhos, pois acredita que uma família forte é o melhor tipo de família.
O amor dele por Joanna
Ele tinha um amor extremamente próximo por Joanna e, provavelmente, não queria se casar novamente. Isso é mencionado várias vezes no texto, mas para escolher um exemplo particularmente revelador:
In 263 AC, after a year as the King's Hand, Ser Tywin married his beautiful young cousin Joanna Lannister, who had come to King's Landing in 259 AC for the coronation of King Jaehaerys II and remained thereafter as a ladyin-waiting to Princess (later Queen) Rhaella. The bride and groom had known each other since they were children together at Casterly Rock. Though Tywin Lannister was not a man given to public display, it is said that his love for his lady wife was deep and long-abiding. "Only Lady Joanna truly knows the man beneath the armor," Grand Maester Pycelle wrote the Citadel, "and all his smiles belong to her and her alone. I do avow that I have even observed her make him laugh, not once, but upon three separate occasions!"
The World of Ice and Fire, The Targaryen Kings: Aerys II
Na verdade, não seria errado dizer que uma parte dele morreu naquele dia e ele provavelmente estava de luto profundo por algum tempo e, portanto, provavelmente não queria.
A queer time to come visiting. His mother had died giving him birth, so the Martells would have found the Rock deep in mourning. His father especially. Lord Tywin seldom spoke of his wife, but Tyrion had heard his uncles talk of the love between them. In those days, his father had been Aerys's Hand, and many people said that Lord Tywin Lannister ruled the Seven Kingdoms, but Lady Joanna ruled Lord Tywin. "He was not the same man after she died, Imp," his Uncle Gery told him once. "The best part of him died with her." Gerion had been the youngest of Lord Tytos Lannister's four sons, and the uncle Tyrion liked best.
A Storm of Swords, Tyrion V
There was a worm inside the apple, though, for the growing madness of King Aerys II Targaryen soon imperiled all that Tywin Lannister sought to build. His lordship suffered great personal loss as well, for his beloved wife, Lady Joanna, died in 273 AC whilst giving birth to a hideously deformed child. With her death, Grand Maester Pycelle observes, the joy went out of Tywin Lannister, yet still he persisted in his duty.
The World of Ice and Fire, The Westerlands: House Lannister Under the Dragons
Seus herdeiros
Ele já tinha herdeiros neste momento e Jaime no 8 já estava mostrando sinais de se tornar um forte guerreiro. Como tal, ele não estava indo a lugar algum naquele momento, então, na mente de Tywin, ele provavelmente não tinha preocupações com Jaime herdar o Rock. É claro que foi somente quando Aerys o desprezou que qualquer preocupação teria mostrado.
Day by day and year by year, Aerys II turned ever more against his own Hand, the friend of his childhood, subjecting him to a succession of reproofs, reverses, and humiliations. All this Lord Tywin endured, but when the king made his son and heir, Ser Jaime, a knight of the Kingsguard, he could abide it no longer. Lord Tywin at last resigned the Handship in 281 AC.
The World of Ice and Fire, The Westerlands: House Lannister Under the Dragons
Nesse momento, Jaime e Cersei eram o 17ish, se eu trabalhei corretamente, e talvez Tywin não quisesse criar duas facções rivais em seus filhos, pois ele acredita que os Lannister são a Casa mais poderosa e mais forte.
Também vale a pena notar que, neste momento, se ele se casasse novamente, haveria uma forte possibilidade de que qualquer novo herdeiro que herrasse o Rock pudesse ser um jovem Lorde e parece altamente provável que Tywin compartilhe a visão de Roose sobre os jovens Lordes. Ele quase certamente não o desejaria, apesar de ser um jovem Senhor e a Mão mais jovem.
"And won't my bastard love that? Lady Walda is a Frey, and she has a fertile feel to her. I have become oddly fond of my fat little wife. The two before her never made a sound in bed, but this one squeals and shudders. I find that quite endearing. If she pops out sons the way she pops in tarts, the Dreadfort will soon be overrun with Boltons. Ramsay will kill them all, of course. That's for the best. I will not live long enough to see new sons to manhood, and boy lords are the bane of any House. Walda will grieve to see them die, though."
A Dance with Dragons, Reek III