I just find these little things difficult to deal with. I hate confrontation and I find myself having to discuss/boss around someone besides my kids.
I'd say, make sure she has a pair of shoes by the back door...by A) buying her a pair of cheap plastic flops or B) telling her to buy herself an extra pair.
Personally, I would just pick up a pair and tell her it was for her.
It's a little annoying, in a way you wouldnt expect, to have someone use your stuff without asking. Ours has worn my daughters flops without asking. Oops. I never say anything.
The eating thing is odd. We actually invited our maid to eat with us but she doesnt. Some of my kids are super slow eaters and she'll have the whole kitchen cleaned and still waiting in the wet kitchen for them to finish. I'll call her in and tell her she can eat, but she'll usually just go out and tell me she's cleaning. Especially if my husband is home.
Anyway, it shouldnt be hard to tell her to eat without you. To eat first, or whatever. Our maid would never eat before us. She ALWAYS waits until we've eaten. But making your preference known should fix that. She was probably used to her old employer.
As for the kids, to me that is the trickiest part. Our maid told the kids they could do something the other day, and she told them not to tell me. They were saying..."Miss P, if we do that our mom will spank us." LOL. And she said, "Shhh! It's okay." My older daughter had to exert her authority to get her to stop. Bizarre. (And she has NO AUTHORITY with my kids...she does not do ANY child care.)
I have to talk to her about that! She's on vacation and I figured it was just a fluke because she was so excited about vacation.
That being said, if I were you I would write her a note.
Seriously.
I would just tell her that she can't say negative stuff in front of my children about them. That you understand that currently they are hard to deal with as they've had a lot of transition. But she can help by XYZ. That will help them too.
I actually did that a while back when she was giving them snacks at all hours and places. I just wrote her a note letting her know that usually we do designated eating times and places (the table!) and that moving has been kind of hard on them, etc etc etc. Now she only does it with the baby. Who we promptly pick up and place in the high chair.