I agree completely with pink and dixie. I remember reading one of the threads regarding the cory, in which you said water conditions were improving after being neglected for a time, it was mentioned by others in those threads that water quality could be the issue, and using chemicals to correct poor water quality is never a good plan... it just puts more stress on the fish and doesn't really do the job, in spite of claims.
I'm saying this with only the best of intentions for you and your cory and not out of unkindness or criticism.
Regarding water quaility issues, I speak from experience as I had spikes in parameters, elevated ammonia and then nitrites in a mini cycle, and this is even in spite of me trying to keep excellent water quality. I had too much gravel in my 10 gallon and did too much stirring up of the gunk on one of the water changes, which caused a mini cycle, and I didn't know for about a day that I had over .25 Nitrites in the tank. I normally had 0. The effects of the spike from the mini-cycle hit my Brochis, which is a cory, very hard.
He developed a bacterial infection, I didn't notice until he had septiciemia, which presented as red splotches and a thin red streak on his body.
He went into a small hospital tank and had 80=90% water changes daily. I did use Maracy and Maracyn II that fight gram negative and gram positive bacterial infection, and he began to improve within 36 hours.
He recovered fully, but that is because obviously it was bacterial and whatever kind it was sensitive to those meds, but as much as the meds I believe the water changes helped him dramatically.
Since you have tried antibiotics and he is still having problems, I would hold off on any more chemotherapy.
At this point I think pristine water, daily big water changes are needed to help his immune system fight this, whatever it is that he has.
After a day or two of being in absolutely perfect water conditions you might try dosing with Melafix, since it is a natural, supposedly soothing, treatment that has some antibacterial action.
The only reason I suggest this is that I remember reading a thread in which one of the AC members, who had been doing this a very long time based on the join date and number of posts, who said clean water and Melafix was all they ever used and had cured many cases of bacterial illnesses.
Having made this suggestion, I welcome correction by anyone with more experience than me, if it may be the consensus that even Melafix, at this point, may be too much stress for the poor fish to handle.
Regarding your father's sick tank: The best you could do is tactfully offer to do maintenance for him. Tell him you want the experience, that you think it will help you become a better fishkeeper. If he will allow it, do weekly, water changes, vacuuming gently in a different area each week so as not to stirr up too much for the occupants to handle. You might try to do about 25% at first, in case his tank has
"Old tank syndrome". Later, bigger water changes would be good, on a weekly basis.
Test the water with a liquid test kit. See what the parameters are in his tank and yours. Nothing replaces good hard work on your part to maintain clean water for your fish.
If they begin to have excellent water conditions then maybe they may start to fight off whatever may be in the tank. A weekly dose of Melafix in his tank may help if there is a bacterial infection going on, though it certainly may not be enough to do any good if there is a serious bacterial infection in the tank because Melafix is not an antibiotic.
Your descriptions of his fish sound like bacterial infection. I'm sorry for his fish, that he doesn't practice better care for them. You, however, can try to act on their behalf, if he will let you.