You can just do what I did this year with one player who had a parent on her case while at bat. I told her that her mom means well but does not know what she is talking about and gave proper instruction. I went on to tell her that her Mom meant well but that if she wanted to hit well she should listen to me while on the field and not her mom.
Response a week later: Sure coach she has to listen to you while she is on the field....BUT....She has to live with me.
This player is no longer on my team. Here is your SIGN!!!! So sad for the player but I could no longer manage her mom.
Otherwise....Breathe....Move on. This is gonna happen no matter what.
The way you characterized this it I would not have approached it the way either of you did.
If you want DD to change how she swings me as a parent needs to be educated or you are fighting a losing battle. I spend more time working with her then her coaches and have more influence. I do not provide advice during a game but you will have her head spinning with us practicing one thing and you have her trying to do something different in the games.