She is probably feeling as awkward and uncomfortable as you are and doesnt know what to do with herself.
It sounds like she is desperate to be helpful but doesn't know what to do for the best.
You see the threads on here - "mil is only 10 minutes away sitting in her house and I am here struggling on my own with a 4 week old baby"
Can you explain to her what you have said here in a nice way with a little bit of exaggeration of the truth.
Just that you are struggling with feeding and as much as you love her you don't feel comfortable with feeding in front of her. You are looking to get into a routine
You want to try to do it all on your own - but you would rather try it when she is available and only 10 minutes away if you need her.
Promise to phone her the second you need her.
Maybe suggest that tomorrow she comes over for lunch - then ask her to get some nice bread or something so she spends the morning shopping.
She could then maybe take baby for a walk while you can have a shower in peace/watch tv/ whatever.
In a few months when you have a teething baby and you haven't slept for days you'll appreciate her help then !!