If can afford the house on your own you need to stay there and suggest she can leave anytime she wants, she's not chained to the house. Don't try to stop her, reason with her, or guilt her into staying. It's a waste of time, looks needy and weak, and is counter productive.
About the kids, you have rights, as does she. See a lawyer and know your rights. Try to keep them in the house and just visit her for her time with them. If she cares about them she will let them stay in their home for minimal disruption in their lives (doubtful that she really cares at this time).
Don't be afraid of her leaving, she's already gone mentally anyway. Drop the rope, GAL, and be the best dad and person you can be.
Me:49 W:45 M:19 T:22 EA confirmed and ended 8/2014 S:19,17 D:9,5