I wouldn’t have filed any legal papers. just wait until she leaves and change the locks. If she calls the cops, just tell them she was a “babysitter” for a week and never lived there. her job was over, and she left on her own, but they caught this criminal woman illegally trying break in & trying to burglarize their home. It’s their word against hers.
This approach can work but is dangerous.
If you end up in court, which you may, it is all about who has the most plausible story. The nanny might make a pretty good case.
Plus it's not a good strategy to commit perjury in court. People try and do it all the time, but the judge has usually heard it all before. He will see it for what it is.
when it comes to these things, that is playing with fire... they already messed up big... now they need to get a lawyer to do their paperwork... enough of this Craig's List-trying-to-save-a-few-bucks-and-trying-to-do-our-own-paperwork shenanigans...