From my experience, there are two kinds of people:

• The kinds who are friends with their ex(s) and have them as normal parts of their life, accepted with their current partner.
• The kinds who are not friends with their ex(s) and cut off to have a clean break and start a new life with their new partner.

I think you should decide which person you are.

Personally for me, I could never go back to "just friends" with someone I have been intimate with. But I won't judge those who do.

It sounds like this ex is going to be a part of her life regardless. Only you can decide whether or not that's enough for you to stay and endure it or simply leave and find someone who feels the same as you do.

FWIW, I think you're both mis-matched. She won't drop the ex but you will always have the insecurity of having him around, though her confusion over your reaction also makes me a little suspect as she should have some degree of empathy. Not everyone is okay with having an ex as a friend. Likewise, you cannot control her by making her choose between mentioning this friend to spare your feelings. You had already broken up before, maybe things aren't as good as you think?

Not being harsh, but just being honest.