The cancer that your father has is the most common form, and it couldn't get any better than stage 0. However, your father is experiencing what is BAD about this cancer...while it is Stage 0 (which means that it has not gone "anywhere") this cancer tends to come back over and over. It is notorious for this. BCG is what they use when it starts returning, but it isn't always effective in this situation. It is probable that this is why they have gone to a clinical trial of such a drug.
You will find, if you read a bit on this website and Forum, that we are always championing second opinions. We do it so often that it has almost become a joke!
But, seriously, a second opinion would seem very pertinent here; your father has a situation that could become more serious as the tumors continually re-appear, BCG has not been effective, and he is not doing well on the experimental treatment.
He is close enough to NYC to seek a second opinion at Sloan-Kettering, or Boston at Mass General, or Baltimore at Johns Hopkins. There may well be other options that would be better for your father's circumstances. At least he would know what options might exist.
I do understand that it is difficult sometimes when parents do not want to "worry" their children. But you are now entering a medical field and have some knowledge and advice to offer. With the cancer returning, this is not a situation to be ignored.
My thoughts and best wishes are with you.
Sara Anne