You're a little hard on her. Aside from sexual abuse, she had her future mother in law force her dad to kill her wolf. Then her Finance's uncle/dad stabbed her dad in the leg. Then her fiance beheaded her father in front of her, beats her and mocks her and later casts her aside for Margaery. His head is put on a spike and he torments her with it. She was then forced to marry he former fiance's dwarf uncle, a notorious drunk and whore monger. The only good luck she had was that said Dwarf was damned nice to her. Even after she escaped King's landing, it doesn't get much better in the Vale where she is nearly sent through the moon door, and then there is Ramsay. The mental abuse heaped on her is pretty extreme.
Sansa got rid of Joffrey, who is about 99% likely to have been a total perv in bed.
As it relates to Tyrion, Sansa's mom did kidnap him and almost got him tossed out the moon door, so Sansa could have given Tyrion a pity bang, considering all her family put him through.
Sansa had to know her aunt was nutty, and that kissing Baelish would set Lysa off. If Sansa didn't know that, then she deserved to go through the moon door. Given how well Sansa performed in front of the Lords of the Vale, I am guessing she knew what was what with her aunt.
I do feel bad for her with Ramsay, but I am guessing Ramsay is going to get his pretty soon, and it won't be pleasant when it happens.
There is really no excuse for lying about Littlefinger's army. That lie puts Jon in danger, and is just bad playing. She has as much a chance of taking over that army as anyone. Anyone willing to take Ser Robin's cherry is going to pretty much get him to do whatever she wants. Hell, she wouldn't even have to bang him, a handy would probably do the trick.
Sansa is about 4 moves away from controlling the North, the Vale and the Riverlands, and she still screws it up.
