I don't know about all that. I'd say you're right that Sansa understands the game better than Jon does, but I don't think that they've pushed her as being one to play it in a selfish way. She only cares about her family and by extension the North. If allying herself with Dany was what she believed was best for the North, I think she'd do it. Sansa doesn't have a problem with distrust or dislike. We've seen her put levels of trust into people that she's had problems with because she knows how to gauge them now. Her problem seems to be specifically with Dany. She's asked more than once "Why her?" She revealed Jon's secret not just because she thinks he's easier to manipulate, but because it would cause problems for Dany. Even if Jon doesn't become king, which Sansa doesn't want to happen anyway, the lineage issue would weaken Dany's claim.