Regardless of guy #2, the relationship with your BF is full of red flags and I would suggest you to end it while you are still young. Then you can perhaps think clearly and decide what to do with guy #2.
I think deep down you know you cannot have a life with your BF; the "affair" is perhaps just a sign that you are 1. looking for what is lacking in the current relationship, and 2. hoping to get found out and cause a breakup because you are not determined enough to just end it.
What I don't understand is why people insist on staying in bad relationships. It is not like you are married, or even living together. Actually when you found out he had another girlfriend 6 months into your relationship, it was time to break up.
I don't know about guy no 2 but I think you should definitely break up w/ no. 1--just because you've had some fun times is no reason to keep hanging on--he's not a good candidate for a long term relationship. his reaction to your DD's father is childish--so he won't go to a baseball game if the father is there. What is he going to do if you stayed together? Not go to her wedding because her dad will be there? His behavior is ridiculous. the part about him having a bad temper is also a big problem to me--why would you want to be with someone who has a bad temper & calls you names? Is that the kind of example you would want to show your DD of what a good relationship is like & how a man should treat her? When you already have a child, you need to be more careful about what kind of person you are involved with because it affects the child (spoken from someone who was in a 2nd marriage to someone who had a mental illness and a bad temper--I had to divorced him because it was affecting my kids very badly).
I think if you were really happy w/ your BF you wouldn't have started things up w/ the new guy--people who are very happy in their relationships usually don't end up in affairs. You haven't really said much about him to know if he's long term or just a diversion, but I definitely think you should end it w/ the BF now.