Can't handle the thought of my baby having a stepmom!

I'm currently 7 months pregnant. The father and I are not together despite the fact that I have strong feelings for him. We've discussed it before pregnancy and I don't think he'd be willing to "try" to make it work, but I'm not sure. We plan to live together after the birth.

He's got a female friend who may become more after I deliver (we agreed no dating while I'm pregnant) and it drives me crazy whenever he's with her. She's offered to baby sit and shown a lot of interest in baby. Now I know that it's likely that won't become anything, but eventually there will be another woman in his life and I am really struggling to handle the thought of another woman being a mother-figure to my son. The thought of the man I love being with someone else is hard enough, but sharing my son is unbearable. How do you ladies who have similar situations handle this? Should I ask if he wants to try to make it work? How?