I don't know that I consider this guy a cheater (did he ever cheat before the breakup?). You broke up with him after satisfying your end of the marriage ultimatum. Even though you talked every day and were both still in love with each other, you were not back together (i.e., to get back together, he would have had to propose to you). It may mean that he needed to get one last thing out of his system before being ready to propose to you. It could mean that he had one last fling (while you were not technically together) and this is what it took to realize that marriage to you IS what he wanted. He was honest with you about the woman and the child even knowing that this could most likely scare you away.

That being said, did they completely fail to use protection altogether or did it simply not work? If the former, get yourself tested now and again in six months. Make him do so as well. Then, ask yourself if you can handle his having on ongoing relationship with this woman and her child. If he is a good guy, this will be a life long financial and emotional commitment....in addition to whatever relationship he has with his first child and its mother and any children you have together. If you can honestly handle this, you may want to give this a try.

Maybe you accept a proposal but condition it on pre-marriage counseling. This will hopefully help all parties involved navigate a very difficult and delicate situation....

But there is probably a reason you have not told your mother. She will eventually find out, and she may be your best ally in determining whether or not this will work for you. She knows both you and your boyfriend, and she seems to like him and have a friendship with him independent of you. If you have people close to you that can provide support you, and you feel that he will understand how you may feel about this from time to time, I don't think it's an open and shut case.