Family drama

So I won’t go into a ton of back story with my family, it’s super complicated, but my daughter (I’ll all her F) is having a birthday party on Saturday (she’s turning 5) and my parents came across the country to visit us.

My mom has always had a huuuge issue with personal boundaries and kind of saying stuff she really shouldn’t say. It’s hard to think of a specific example but hypothetically if a strangers child took something from mine, my mom would take the opportunity to “scold” the other child and say something like “it wasn’t very nice for you to take F’s toy. Please give it back”. She has good intentions but her delivery is cringy, to say the least...

My fiancé has really young cousins (they’re like 4, 7, and 9) and they are extremely bratty and spoiled. Like the 9 year old locked my daughter in a bedroom for 10 minutes the first day they met just to be mean...) my daughter gets along with the other two girls but they can still kinda “be kids” to each other by arguing over toys and being tattletales, yatta, yatta.

How can I tell my mom to stay in her own lane at the birthday party so she doesn’t offend my fiance’s aunt without offending my mom?

For the record. She’s very easily offended. Tonight we went to a restaurant after they flew in and she was being extremely obnoxious and loud and my dad asked her “hey can you keep your voice down?” And my mom replied “if I’m being too loud, I’ll just eat in the car. You can bring my food there.” She does have a lot of unresolved mental health issues that she’s aware of, but doesn’t act responsible for. I don’t want her to get huffy and nasty over my request for her complacency because I don’t want to ruin anything for my dad. But I also know my entire family (besides my mom) will be absolutely embarrassed if she tries to “parent” or control his cousins. How do I say something without breaking the ice?