I went through several months of supervised visits with my children before I got custody back, and I have to be honest and say that the only time I resented the supervision is when I had something to hide. Once I was in recovery and working a program, I had no issue with the supervision. I understood I had messed up and I needed to prove myself, I was happy to do it, as all I wanted was to show that I had changed. I'm not saying this is how your children's father should feel this is only my experience.
As for the methadone, it's not the only drug that's handed out that you can be considered DUI for. That being said, without a doubt when I was in methadone maintenance treatment, I was high. I was on a rediculously high dose for my weight and if I got still I nodded out. I wasn't taking benzos or anything on top just the methadone. It really depends on the individual as to how they metabolize the dose and things like that. Perhaps you could speak with the people who supervise the visits and see if he appears to be under the influence during the visits.