
As I assume he came in on Pet Passport, he can travel back under that scheme, but I think he will also need an utd health certificate.
As far as the paperwork with the KC is concerned, you will need an Export Pedigree so the breeder in Hungary can apply to her KC to have him transferred (back) into her name, unless she decides to leave him in your name (and assuming you have transferred him into your name?)?
I sympathise with your situation between the males - I had to home a boy we'd run on from an all-male litter (Sods Law when I wanted another bitch). He hit 2 and started challenging his uncle, despite only the uncle being used at stud. Try as I did, to get them to resolve their issues, there was no way the younger one was going to back off so in the end, I had to find him another home, so peace could return to our small pack. It was heartbreaking, but for the best and he was fine. When we went to check, a few months later, he acknowledged me, and went right back to playing with his two bitches!! Result.