But I'm not sure how successful she would be, but she can certainly try.  But honestly, your FDH will receive the information, and what he does with it is largely out of her control.

I've been removed off checkout lists and approved to take to the doctor lists by her before... DH just adds me back. Ultimately it's none of her business. If your DH trusts you and gives you permission, and shows them to you, there really isn't anything she can do.

She could try and there is a good chance she would be able to do so depending on where you are. All she has to do is remind them that she is the legal guardian and you are not. She for sure couldn’t stop your partner without an order but HIPPA violations cost A LOT and a hospital won’t want to take the risk. Same with a school. Again she and he are legal guardians and of equal status. They both can say someone else can but if there is an agrument there is a good chance the location with go with caution and just remove you for safety. 

You can be included on a release form, but she can have you removed. Many doctors anymore require you to update your list of who is approved to receive information at each visit.

However, your FDH isn't going to just be able to say over the phone "tell her". He will have to put it in writing. But, just as he can add you, BM can remove you. She can remove him, too, but if he has a legal right to records, they can't (or shouldn't) deny him access.

Its a little different. I have sole legal and physical custody of DS16 so yes I can have his step mom and even bio dad removed from access to all records school and medical. Not that it would matter because bio dad hasn't seen DS in 6 months again and has no intention of seeing him.