One thing you are going to have to decide is if he is the person for you, he cheats on you not once but twice with the same woman and then breaks up with you to be with her, he didn't care that he was hurting you (the mother of his child) in the process, if you take him back without making him earn your trust back things will not change because you are making it too easy for him to come back instead of making him prove he deserves a second chance and since he hasn't officially broken up with this woman he hasn't proved to you that he deserves to be back in your life because he is still going between the two of you. Why is he mad at you for something he should have told his girl about? You did what you thought you had to do because you were tired of him going between the two of you.
One thing you could do is apologize to him and tell him that you shouldn't have interfered in his relationship and that you should have allowed him to make that decision of when and how to tell her. That is pretty much the only thing you can do right now and then give him a cooling off period if he is that furious with you it is going to take some time for him to get over what you did, he probably feels that you stabbed him in the back. Explain to him that you were angry because he kept going between the two of you and you didn't know what else to do and that you felt like he had backed you into a corner.
You are really going to have to sit down and think and ask yourself;
1. Is he really worth all of this that you have to go through to be with him?
2. Does he deserve to have you in his life after everything he has done to you?
3. Will you be able to trust him again after all of this?
4. Will he continue to sleep with her if you get back together behind your back?
5. Would he be willing to show you and prove to you he deserves a second chance and not start seeing someone during that time?
6. Why did he go to this woman in the first place, what went wrong?
7. What is going to reassure me this won't happen again?
Until you have answer to those questions your relationship will be pretty much the same and you will be miserable because every time he leaves the house you are going to wonder where he is and if he is with the other woman. Trust is a huge part of a relationship and without trust you are always going to be in doubt. As far as him being mad because of you telling the woman he was with you during the time they dated that was something that needed to be told. Even though he should have been the one to tell her but I don't know if he would have ever told her, so I wouldn't feel bad about telling the truth and that is all you did was tell the truth.