Uchiyamada is the vice-principal (or principal) of the school Onizuka teaches at. From day one, he hated Onizuka and his hatred for him only seems to grow. This is partially justified, as Onizuka caught him groping Fuyutsuki on the bus and beat him for it; then, Onizuka performed a german suplex on him, for calling expelled students trash. Onizuka also frequently seems to (inadvertently) destroy his precious Toyota Cresta. His hatred for Onizuka gradually grows more and more unhinged. Eventually though, he does let go of his hatred, realising he was no longer the enthusiastic teacher he was in the past. Onizuka still gets on his nerves, but he doesn’t call him a bad teacher anymore.
He was, for a while, obsessed with the reputation of the school, willing to fire teachers and expel students if it meant saving the schools image.
At home, he feels like his family takes him for granted, not treating him with much respect (despite the fact he’s the one keeping them afloat). His obsession with the Cresta is born from the idea he can fix all his family ideas by going on a hot springs trip with it, although later it seems to be based on the fact it keeps getting destroyed (If I got it right, he goes through 7 Crestas over the course of the series).