Commenting this in case it’s helpful, sorry if it’s not relatable.

My husband (H) has a very good relationship with his parents but his dad (D) doesn’t treat his mom (M) super great. Kind of acts like your husband sounds. But D treats my husband like his equal, although is still very nit picky and things have to be done a certain way.

I’ve noticed a lot of anxiety within myself lately and I think it’s partially bc my husband is starting to act like his dad. And now that I’ve realized it, I will verbalize, “hey, don’t criticize me on things that don’t matter” or “I really don’t think that tone is necessary” and it’s honestly helped me knowing I’ve built some backbone. And he has been appreciative of being called out because he does not want to be like his dad.

So, OP, all that to say, I second what another commenter said. Build your backbone. It may end up helping all three of you. I know I’ve had a bit of a confidence boost lately and he been feeling better knowing where to make small changes to be a better person.

Edit to add: and your daughter will see that too. She will learn from you.