Advice for a single mom?

Mitzi
I caught my boyfriend emailing his ex less than two weeks after our baby was born. He was basically begging her for sex. Literally begging. According to her, he was cheating on me with her throughout our whole relationship. He, of course, says it isn't true. He says they would talk about hooking up but it wouldn't happen. She's known to be a liar so I don't know who to believe. I broke up with him as soon as I caught him and don't plan on getting back with him. After I told him to stop talking to her, he kept doing it for another two months.  I just want to know if I should give him another chance so that my daughter can grow up with both parents around. But I just don't trust him so I don't see our relationship being healthy which wouldn't be good fort daughter either. Any advice?