ADVICE PLEASE

So I recently gave birth, about 4 months ago, to my son, with my current boyfriend, being the father. We've been together for about a year and half, off and on because I needed to see what I wanted in life and if I was going to be with him, I wanted him to be a better man for our son. 
So he moved to Arizona while I was pregnant and almost everyday he would say how much he wished we were back together, only wanted me, only loved me, and I was like leave me alone, move on, but to my understanding, during that time, he was all alone. 
Well he came for a visit around November for one of the ultrasounds and at that point we really started to talk and figure what was up. We got back together because I thought he was really just waiting to be with me again. 
So, he leaves and we fight here and there, I really try to be good because I felt like I couldn't piss him off. 
He ends up coming back a week before our son is born. He moves in with a guy my mom works with. 
Now everything is splendid, I have my boyfriend here with me, and newborn. 
But, about 2 months ago, I found out some stupid shit. 
The whole entire time he was telling me he was alone and so sad and only wanted me in his life he did the following 
1. slept with another girl(mind you, he was a virgin before we got together) 
2. Constantly talked to multiple women
3. Told them he loved them
4. Sexted 
5. Told all of them that the baby was probably not his 
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Also, that isn't even the worse of it, about 3 weeks ago, I found out something else out! 
After we got back together, and he moved back to Arizona. 
He met a girl named Sasha at work, she knew about me, and they had an affair for 3 months. The last time he saw her was their farewell before he got on the plane.
He had cheated on me before, when we first started dating and I kinda shrugged it off.
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But here's the deal, I know many of you are going to be like "what the hell, why are you still with him" 
I'm trying for my son. I want my son to have a family that isn't broken. 
I also don't think my boyfriend will make it, if we break up, he needs my motivation to do anything, I feel like his mother. 
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But what should I do?