Based on your posts and despite the costs, one of you need to move out for the emotional well being of you and the kids. Things are unlikely to improve while living under the same roof.
If she won't move then you need to. Get yourself organised, and make it happen. If you move, after a few weeks it will seem like a breath of fresh air. You'll still be sad, and sad for some time, but should feel the beginnings of a new life emerging from the dark fog surrounding you now.
If money is an issue for you recommend you tell her to move out as your first choice and give her a set time to do it by (2-4 weeks). If she doesn't move, get yourself organised and arrange things in advance (eg deposit money, centrelink etc) and start thinking about child support to be paid by her. If she gets payslips get evidence ready for a battle over child support.