Are you in the UK?
Will you have a private room?
Would you be happy that your DH and his Dad and SMIL saw your babe without you?
Can you slip the midwife some 'grease' so that she can keep this MIL at bay and not allow her in to see you?
Just tell the midwife that this woman upsets you too much and you don't want to see her, or have her admitted to the ward / room.
The midwife / nurse can come up with excuses: No visitors because....She's sleeping / has an infection / is feeding / at a bf class / the physio / lactation consultant is with her.... endless excuses may be used and re-used!
Or the nurse can be asked to stay in the room, or that she comes in after three minutes or so to order you to use the bedpan! Get friendly with your post birth nursing staff - box of chocolates are a must.
There is a solution.
Focus on getting the birth over and done with and the feeding sorted out.
YOu never know, your midwife / DH may never leave your side if you ask her / him to 'protect' you from her.
Announce the birth of your babe when you are home and sorted out..
FWIW I've never got this "I must view the babe on it's first day" thing that seems to strike - it's very unsettling for babe and Mum.
You don't have to have her there - just enrol people to help you - remember you are under the care of the doctors and nurses there - you DO have rights about visitors if they effect your mental health, and they DO have an obligation and a duty of care to see that you are not damaged by your stay under their care.
Get them to help you, talk to them about your strategy.
Is there counselling available for you?
Figure out your strategy to keep this woman at arms length if you choose it so, and good luck!