I agree that maybe Bun-Bun doesn't have cancer, but again, he shall be seen by a SAVY vet. When my bunny MILU got sick, I took him to all vets who said they'd treat bunnies, but they didn't even know what he had. Then they said all possible sorts of stupid things, like he's "stressed", it's his stomach, etc. He had a dental issue - and I only found out because of great advice from everybody here of Rabbits Online. I'm very grateful because they're the ones who helped him.
Now what I'd do is:
1- taking your bun to a good vet,
2- maybe you could also post pics/exams you have available in the infirmary section here. Maybe someone can help and tell you what the issue looks like.
3- maybe you can keep Rocko in a separate area of your home... you talk like you want to give him love too, you said you treat well all your pets, and that your parents help with food... now it would be cool even for you to keep him, learn his ways (my bun in the beginning was nothing compared to my former bun, but after I found out what he liked, and he got to know me better too, he actually turned out to make me happier with him than before...!) Maybe it could work well for you, who knows? Why don't you give Rocko a chance? At least until you find someone who REALLY likes him and wants to keep him, in whom you'd trust? Maybe you can keep one of them in a room (like Bun-bun) and one in the kitchen (Rocko), I don't know.. if you got 2 floors, you can divide territory into floors.. but one thing I'll tell you: all bunnies give back what you give to them. Treat them as "inferior", or "not like the other one" and they'll feel rejected. If you give them unconditional love and you play with them enough, cuddle with them enough, there's no bunny that won't be really nice and soft and warm-hearted! Good luck!