I know this is my character and I'm supposed to decide what is right/wrong, I'd just like some insight or suggestions.

A Redoran stole something from his family, and now he's trying to get it back?

He's a Redguard with a semi-tribal, very proud background but is at the same time relatively cultured. I'm thinking maybe he joins House Redoran and like for some kind of extra great quest success or some kind of great service they give him access to the vault.

The redoran pushed him to the edge and the only way for him to become sane again is to steal everything in the redoran vault.