A few months after writing this post, I feel much better. Paradoxically, by admitting to myself that I just don't like this woman (and she very probably doesn't like me either), instead of tying myself in knots trying to logic my way out of negative feelings.

She has the very character traits that just happen to grate on me (bossiness, competitiveness). And elder care is a tricky situation for a family generally in any case.

However, I realize I can not like her while also being grateful for the care she's shown for my father and grateful that my brother has a great partner.

It's mutual civility that counts in this situation, I think.