I think you just need to explain your situation and ask. When we were in hospital, we were originally going to have a c/s. We'd wrote in our quickly put together birth plan for DH and IM to be there. I wanted DH to stay with bub and the IM to stay with me (I had a thing - I did NOT want to be left alone at any time). One of the doctors objected, so my IM went and talked to someone else to get approval.

I'd start talking to your OB about your birth plan now, including this and other things like having skin to skin contact, bub being with you in recovery, no formula/sugar water feeding (& expressing colostrum before hand) or other things you'd like.