Well naturally, you wouldn't want to be the one conducting the supervision. It's difficult and costly to get a third party visitation center, in place. Those are usually good for children at risk due to extenuating circumstances. By you, being the supervisor, it keeps you at an arms length, to him. Though statistics may show, abuse relationships can trickle down, to the children, one doesn't want to appear, as not fostering the non custodial parents relationship with the children.
Also, if he's going to take, just one, this time, he needs to share that one on one time. I do question, his parental rights to visit a child that isn't his, biologically?

Hope you can reach an amicable solution. You are allowed to file for child support, even if other papers aren't filed, since he's moved out.

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