Re: Who should leave
Talk to a lawyer, file for divorce before she does, grounds of adultery. Don't allow her to get anything. She does not deserve it. However, I would recommend that you look for a place and leave her with the children. Do what is in the best interest of the children. If she is a good mother, let her keep the children. Whatever happened between you two should never spill over to the children.
While you guys are working that out, make sure to sit down and make a parenting plan. Visitation, child support, and more importantly how you will interact with each other, and who's duty will be to do what, in order to ensure the children are not anymore negatively impacted by the adults decisions.