1. No cheating case is made out against him. The legal meaning of cheating is a far cry from the meaning which is ascribed to it in common parlance by laymen.
2. If he has an extra marital affair, which you have found out, you can file for divorce against him if you have the required degree of proof. This apart, you can also file a case for domestic violence to claim compensation for the domestic violence suffered by you.
3. The right to maintenance can be claimed by you and your children. He can contest your claim to maintenance if you are earning on her own.
4. You are free to leave your child with him but this will practically disqualify from getting child custody subsequently.
5. He is a free man, so he can run wherever he wants. Even a court of law cannot force him to stay with you. If he evades the summons of the court then an arrest warrant can be got issued against him. Thereafter, it will be the duty of police to search and produce him before the court.