A.V.
You follow the court order, or you get one if you don't have one yet, and you deal with each other mostly in email so that you are not having stupid arguments over the phone. If the CO says he calls once a week during a timeframe, he talks to his children during that timeframe. he can email you anything else. You treat it like a business partnership in the business of raising two children. My DH tells me that when he was getting divorced, his ex would pick fights with him at work, to the point he almost lost his job. He had to learn to pick his battles and not feed her drama. To respond to mysterious voicemails with email and to only reply to the parts of the email that pertained. So if she went off on a rant, he would simply confirm, "The children will be with you on x weekend, per the agreed adjustment to the rotation." It is hard to do, but better in the long run.
And remember, in the long run, his relationship with them is his. We couldn't make DH's ex be a better/more involved/less crazy person. We did the best we could and her behavior stood for itself. We never kept her from her children. She did that herself. If he decides to skip visits or be a check only father, then document everything, make sure you're following the order and won't be held in contempt and just do the best you can for your sons.