Why would Tywin release Sansa or Arya once he has Jaime back?
He's not going to do it, he'd just laugh at you - that's obvious. The fact is, Martin presents this as a rational choice but if she had thought about it at all she would recognise that Jaime has no way to influence Tywin and Tywin has no reason to make a deal, as he already has what he wants - really obvious.
As to there being something wrong with me - well, probably, but I'm not a heartless bastard - I'm just not that monumentally stupid or uselessly sentimental over great distances.
By the time Jaime reached home Sansa could already be dead, and was in fact already gone.
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