Who will be carrying your sons on their health insurance plan? Will the other spouse be paying towards the plan that is being carried by the other spouse?
Definitely, it your situation is now a business deal that has gone completely south. Try to keep your emotions out of the negotiations as much as possible. The calmer you are, the better.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.