Please try to find an alternative sitter. MIL will find out and coerce, bully, guilt or pout to SIL to come over while you’re not there. Then she’ll stay in order to “prove” to you she will always get her way. If you hope to have a relationship with SIL, don’t put her in the middle.

As far as DH giving them pictures, the only thing to really do is ask him to not share pictures and explain why. Hopefully he will honor your request. If he doesn’t sooner or later you’ll find out. She’ll want to rub your nose in it by showing it off on social media, someone will tell you MIL showed them a picture or DH will let it slip. I’m not sure what you could do unfortunately. Hoping for you, he has your back.