If a woman that your fiancé or partner reaches out to your fiancé asking to be friends again and including me would you?

Background on the situation: She is a nurse and my fiancé is a physician. They are co workers so they see each other. Back in October he told me he had slept with her after I questioned why he was always hanging out with her and letting me know till it was happening or afterwards. I asked him it’s ether me or her because I don’t feel like he is giving me my place as the woman in his life. He told me he would not give up his friendship because she was family. He did it anyways but i could tell he was bothered. Recently he graduated from his Residency and she was at the graduation. Ceremony. I didn’t know she was there or what she looks like so I wouldn’t have known either way. Everyone was taking pics with all the graduates and coworkers he took pics with her and I didn’t know. I could tell he was hiding something but I asked about it later at home. He told me his friend told him that girl was there and he didn’t see her. I asked him “is that it?” He said yes. The next day I could tell he was hiding something still so I kept bugging and he admitted to taking pics. He said t was no big deal but if it wasn’t then why hide it?

Last incident: So two nights ago he showed me a text of her asking to be friends and wanting to be friends with me too. I found t incredibly naive of this woman to have a partner of her own and still text an engaged man to be friends with her knowing they’ve had sex before even if it was once and a while back. I told him thank you for trusting me in letting me know and I asked him what he wanted to do he said nothing so we dropped it and went to sleep. Yesterday he brings it up and asks me what he should do or text her back? Automatically I knew something was up. I asked him what he wanted and he said for all of us to be friends. I told him if he has ever heard of a man having dinner with an ex hookup/friend and fiancé. I let him know I would suck it up but let him know this wasn’t a family man move. When you have a family you give up things but you gain something greater in return. Also, I asked him if he though if his father,brothers, or successfully married friends ever did that to their partners He told me no and realized it was dumb but now I want to meet her. Because well why the hell does this woman keep popping up in our conversations in our entire relationship? What do I do? Do I drop it, tell her to leave us alone, embrace it, or what. I seriously need advice! Please help me out we are trying for our first baby (my second) on top of all of this and I’m stressing out bad

UPDATE: just to be clear he never cheated on me. They had had sed as a one time thing about half a year before we even met. But he’s always felt close to her and he stopped talking to her completely. He took the pics with her since hey had to because they work together as all the other doctors he just hid it to prevent me getting upset since we still had to go to one of his bosses after party where all the other physicians were too.

I let him know I want to have dinner tonight and talk to her face to face. I want to ask her three questions.

1. Does your boyfriend know you are texting my fiancé and asking for a friendship?

2. Do you think it is morally okay for a a woman with a partner to text another engaged man that you’ve previously had a relationship with?

3. How would you feel if you were in my situation?

And please ladies help me think of any more questions. I am going to get the information from the horses mouth because I am tired of this being an issue.