Legal Question in Real Estate Law in California

Re: Can I be charged 'rent' to live in a house left to me in my mother's will?

Absent a contract with the other co-owner providing for rent, no.

All co-owners (as tenants in common or joint tenants) of real property have a shared, undivided right to possession of the entire parcel. That makes them kind of involuntary roommates. Since each has the right to possess the entire property, neither co-owner can charge or collect rent to/from the other.

This basic circumstance of co-ownership can be modified by contract between the co-owners. Also, neither is entitled to gain possession or oust the other from possession by force, threat or other breach of the peace. If one co-owner gets into possession and tries to exclude the other, the solution is a lawsuit, not a war.

An executor is an officer of the court and a fiduciary of the heirs, and this kind of conduct, while probably based on ignorance rather than malice, is a miscarriage of the duties of office. You don't say so, but your brother is perhaps also sole trustee of the trust. You should gently counsel him to learn more about his duties and responsibilities, or to hire a lawyer to coach him so he stays out of trouble.