There is nothing wrong with a 50/50 arrangement, and your kids leaving their house to go to your wife's new place, if it's part of a legal agreement.
For your wife to unilaterally make the decision to leave, and simply take them with her, is an entirely different matter.
Have you thought about a restraining order against OM being in contact with your kids? You should.
Again, I implore you to seek legal counsel. A free initial consultation, or do you have an Employee Assistance Program at work that includes any free or low-cost legal benefits? If not, then borrow from a family member if you have to -- you need to protect yourself.
