I need him to leave the house

He has admitted to the adultery.
I have told him I want a divorce but he says he won’t leave the house.
I have two young children. Money is tight.
Do I have legal recourse to make him leave and let the children and me live in the house?
thanks

Adultery is grounds for a what is called a divorce from bed and board. This is different from an absolute divorce ( as you must be separated for a year before you can file that action) and is a type of action that allows a court to order separation of the parties: ie getting a spouse to leave the home.
You should consult with an attorney to formulate a plan of action in the near future.

What if there has been adultery on both sides, but he won’t agree to a separation unless he takes one of the kids? I don’t want him to have them, (he’s not mentally stable, he’s verbally abusive and he doesn’t have a job) but I don’t know how to keep him from taking 1. What are my options?

You need to meet with a lawyer to create a plan of action. You must be living separate and apart before you can file suit, so it may be that you will have to leave the house to get the ball rolling. I would suggest you do so soon to ensure the children are protected.

Since both of you have admitted (?) to adultery, then either one of you could file a divorce from bed and board to get the other one out. Also, there is a host of other reasons (fault) that can be used to force one spouse out of the house. Only leave your home if you and/or the children are in danger.

Also, remember adultery is a bar to alimony if the dependent spouse has committed adultery. In your case, with both at fault, it’s the Court’s discretion.

It may be best if your respective attorneys can work all of this out for you rather than going through the Court system. You probably need a lawyer.