Do what's best for your child and you. Find someone who respects you and your marriage and whom you can trust. Otherwise, it's not going to be a good environment to raise your child.
The two of you should see a therapist as soon as possible. Maybe your marriage can be saved.
Do you love each other? Talk to him, told him to stop contacting that woman if he still care about you and your children. If he do so, then, I know it's hard, try to build your broken trust with him. If he don't, then, I'm afraid that, you should make allowance between yours and your children lives.
I see, does he still love you? Well, I can't say what do you have to do. But, I advise that, if you're not religious, and divorce's not complicated enough, then go for it. Start a new life with someone who REALLY cares and loves you and your children just the way you are. Your children wouldn't be happy if they find out their dad doesn't love their mum, and cheated from her. They'd need a loving and caring dad. Believe me, child's familyhood affects their future and characteristic.
You should file for a divorce. Get a job and leave the jerk !
Do you love him ?
You should leave. He doesn't love you as you deserve to be loved. I mean, who treats their wife this way ? You gave him a child ! All you're doing is just to preserve your couple.