Should I move out or forgive him?

I am 28 years old and have been in a relationship with a 33-year-old man for six years. We have been cohabiting and have an 18-month-old son. However, my boyfriend avoids any talk about a wedding or introduction, claiming he has no money, yet he is not poor. I guess he just does not want commitment. Recently, he tried to date my 21-year-old sister. My sister told me that day, he went to her hostel and asked her out, but she refused. I immediately called him and he lied about where he was.
I later met my sister and she called him with the phone on speaker. I heard him plead with her not to tell me about what was going on between them. I confronted him about the issue after two days, but he denied everything. I feel betrayed. He sent me messages apologising, but does not want to talk about it. Should I move out or forgive him?