Hi mama gaga I'm sorry you are getting a hard time here as I think you are being more than fair with your au pair.
Here's my take on this. I had a lot of help with my children when they were pre school age. I was present most of the time but sometimes I wasn't as I wasn't well. I had some lovely girls helping me , some I'm still friendly with and some nightmares.
I had one in particular where when she was around my child that had the most challenging behaviour would often have little accidents. One particular one was when he came in screaming and she told me he had caught his fingers in the car door.
Another time my husband came home from work and him and this girl were putting the children in their car seats and she slapped my child.
She was told not to come back.
If she is doing that in front of a parent what was she doing when we were out of ear shot...ie the car door slam incident.
My gut feeling is if you were to set up a baby cam I think you might be horrified to find that she was being rough with your child or downright cruel. If she is not feeding your child thats cruel . If shes not doing that in front of your 11 year old who can tell you what is she doing to your screaming baby when the others are in their rooms getting dressed.
She isn't suitable for baby minding. Let her go. She might be ok with a toddler but definitely no child younger than that.
Another suggestion is to pay someone to come to your home at 8 to do those duties. My friend went back to work and got a much older lady whose only responsibility was to play and take care of the baby in my friends home. My DIL would jump at the chance to earn £120 for ten hours work.
Your au pair is taking you for a ride and is cruel to boot .