Your first prong here is with your H.
Tell him how domineering and over powering she is being, how it isn't normal/natural/acceptable for her H's brother to be doing what isn't his job.
Tell him that there are things women do that are designed to undermine other women, and men don't necessarily pick up on. She is conniving. Men aren't often conniving so don't see it. Her dc are NOT his concern/worry/responsibility, not when it comes at your expense.
From now on, SHE looks after HER dc, and HE stops allowing her the space to get in your lives and undermine you.
Then... call that one out on her pushing and shoving, be a complete bitch if need be:
'Erm excuse me SIL, that's my H I was about to take a photo of, don't shove me aside to play 'let's pretend I have a husband' with someone you're NOT married to. Go find your own'
'I don't appreciate your opinion on if and when I rest. It's my pg, my complications and I don't want to know what your opinion is, much less outside my door disturbing me' 'go find a motorway to play on'
'oh hello SIL, i'm Sabella, have you forgotten my name? Only you greeted everyone else.. I was sure you'd not be intentionally that rude, so thought perhaps you'd got some memory issues...'
You say 'fly home'.. is this creature from a different culture to yours?