Husbands ex is contacting him

I was with my husband for 4 years but broke up with him right before I found out I was pregnant bc he was cheating on me. We stayed separated right up until our baby’s first birthday. He was seeing the woman he cheated on me with during our separation and called things off with her a couple months before we got back together. We have been going to individual therapy as well as marriage counseling together and have been working through our issues. I recently discovered I am pregnant again. News we were both happy to receive. His ex emailed him last week which he showed me. She heard about someone in his family that passed away and wanted to give her condolences. I asked him not to contact her but I knew he would anyway. She is a happy bubbly person and I’m more down to earth and go with the flow and he said that’s why he was attracted to her in the first place but would never want to build a life and family with her. So he did respond and simply told her thank you and to be well. She responded back trying to make basic chit chat and asked him if he’s decided to make things work with me. He told her yes and that he’s happy and that we’re remodeling our home. He ended the msg by wishing her well again and was trying to end the conversation. She kept emailing him and suggested they meet up. He never responded back. He called me up and told me about the emails and showed them to me also. He doesn’t want to get in contact with her again and tell her to stop bc he’s worried he’ll get comfortable and continue speaking with her but he says he’s confident she got the idea and will leave him alone. I’m not so gullible. The fact that she emailed him first of all after almost a year and was flirtatious in her messages even after he told her we’re together says otherwise. I don’t know if I should contact her myself and tell her somehow to back off or if I should leave it alone? I’m not a confrontational person but don’t know what to do. I will kick my husband out of the house permanently if I find out he’s talking with her again. But until that point I want to keep my family together and don’t want to go through another pregnancy like my first and don’t want to drag my children through more heartache and court battles. Any advice is very much appreciated.