Sansa Stark marriage to a Lannister
After Robb's death and Edmure's capture Sansa became an important pawn in the Westerosi chess board. With Brandon and Rickon 'dead' she was heir to the North. She was also heir to the Riverlands especially if Edmure suffered an accident, something that could easily happen since he was brought as hostage to CR. Sansa was an important pawn, that shouldn't be used carefully, something I believe Tywin failed to do.
Under such circumstances Tywin's plan was right. Having the heir of CR marrying
Of course we are pretending that all Sansa's brothers are dead here…
I think you are wrong.
I think Tyrion+Sansa's son would have be accepted as a Lord in the North, because he would be (also) a Stark, whoever his father was… Sansa being the mother would be enough, she's the super-beloved Ned Stark's first daughter and ONLY surviving child (in this scenario). It doesn't matter whether they loved Tyrion or not, it's not Tyrion the one who is supposed to be the heir, it's their son. The