NTA. MIL needs to know who's in charge. I'm a guy, but a few times the women in my family have had tough conversations behind closed doors and sorted out who's running the show.

You're the mother, and you and your husband make the rules. You are never to be bossed around or ridiculed about those rules. If you are 100% sure any caregiver will learn your rules and follow them, you might trust them with your baby. If not, no way.

Rehearse a rough script of what you want to say, get your MIL in private, and be brutally honest about how things are. Put her in her place firmly. It may not be pleasant. But do it.

Then judge her reaction. If she continues with her BS, NEVER trust her with your child alone. If she genuinely accepts your role, there may be able to earn back your trust.