I can't stress this enough - DO NOT MOVE OUT. This is for your protection and for your kids potection, no matter what she says or does. The best way to take care of yourself and kids financially is NOT MOVE OUT.
She is having an affair, you can't trust anything she says or does. She is in crisis mode. She is not looking after your best interests or the children's best interests. She is looking after HER best interests that that does not include YOU.
Please be careful about this and protect yourself. You are the only one looking after you and your kids.