You have to have your daughter's back, DD. What happened is messed up, your daughter may wind up with emotional issues if things continue to go this way, and she could place some blame on you later on for not protecting her from her Mom's emotional abuse.
Lovingly exert your headship from now on. There are times you will be able to compromise. Sometimes you may have to gently overrule yor wife. But don't allow her to abuse your child, understanding that she is doing what she has been taught by the wt idiots. Her intent isn't to hurt her child. Hopefully your daughter doesn't have too much time with Mom when you aren't there so Mom can't manipulate.
I'm sure you can find plenty of credible material online regarding guilt trips and manipulation, including ways to curb it.
You have your work cut out for you. Wishing you all the best.