You are not the problem. You are not crazy for thinking he’ll cheat. He has already betrayed your trust many times. My question to you is this: How many more times will he have to cheat before you believe that he is a cheater?
Yes, you have problems of your own. Threatening to cheat as a pay back is immature and unwise. But that doesn’t absolve him of responsibility for his own actions.
If you didn’t have a child, I would advise you to cut your losses and get out immediately. But since there is a child involved, it may be worth it to give this relationship one more try by getting some counseling. If you do, keep your child’s needs ahead of your own. What kind of relationship do you want your child to grow up believing is a good one? Only stay if you and your partner can make a healthy, respectful relationship with each other.
I wish you well.