A court will not terminate his parental rights absent State involvement. You can and should act to restrict or supervise visitation. Basically you need evidence of serious endangerment.
Consult with an attorney who can adivse you further.
There is no doubt you have a case for maintenance. In such a case the duration of maintenance, the amount of maintenance, termination events and reviewability and modification are all part of what needs to be established.
The over all assets of the marriage is also a factor in maintenance so speak with an expirenced attorney who can help you get the fresh start that you want with the money you need to make it work.
You should review your Custody Judgment to see if has to take her to such events. If so communicate that to him. If not consider modification of the Visitation Order since the move is a change of circumstances.
If money was no object you could file a Petition for Divorce and assert adultry as grounds for the dissolution of the marriage. You could then argue that a DNA test was necessary and that the mother should be added as a party defendant. Very unlikley you would get this relief.