Seems easy to me.
1. If the ball is traditionally "yours" (forehand/backhand on the ad side, forehand on the deuce side) and you call "mine" then your partner should let you have it. Period.
2. If your partner calls "mine" on an overhead, it's theirs. Don't run back to ensure coverage, because you're going to lose on the next shot due to being out of position. Period.
Keep practicing and trust your partner. Eventually you'll get used to who is most comfortable with what shot. Then the "mine" and "yours" will be more consistent. Personally, I say "yours" a lot more than "mine." But if the ball could be played by either of us, I feel that someone should always say something.
Also, you mentioned it as an example, but you say "she's ad, I'm deuce." Ad player takes most of the overheads. Ad player takes most of the middle balls. So who is "taking" balls they shouldn't be taking?