I feel very badly for your child. S/he is an innocent victim in all of this. It's a shame that neither of you thought about your child when you cheated on each other.
That said, while I believe that when there is a child involved, both parties should do all they can to make things work, in your case, I think it's best to divorce. It seems to me that neither of you are capable of keeping your word. If you stay together, it will be the same thing over and over again. Meanwhile, your child will be the one most hurt by both of your actions.
Also, given that you've both cheated, are you sure that the child is yours? You really should have DNA tests done.