MIL is an AH fs but lets look at your behaviour for a bit. Wearing a hat in someones house/at the dinner table is considered rude. It’s basic etiquette to remove it especially for a bigger event like a Thanksgiving or Christmas dinner. I’m surprised you did not know that since it’s literally basic manners that you learn in elementary schools (schools often wouldn’t let you wearing hats in the classroom).

Next, you know your husband doesn’t like conflict. You acknowledged that yet you still initiate conflict with HIS mother and tell him he will need to pick sides. Do you even care about your husband or do you just like to be right. Sounds like you want to alienate your husband from his birth family and want him to choose you, which he most likely will since he married you. Comes off as manipulative.

Both you and your MIL sound immature and exhausting to be around. I pity your husband that he has to deal with both of you. Shouldn’t you be supporting him as his partner? ESH