Legal Question in Real Estate Law in California

Yes, and they should be paying you rent.

No, and you are not entitled to receive rent.

In truth, I am only trying to point out why one-liners frequently don't tell the whole story.

Your facts mention that the property was inherited in a living trust, with you and your brother apparently being the co-beneficiaries. It is the trust that must pay the taxes, and presumably whichever of you is the trustee should be signing and mailing the tax checks twice a year. If you are co-trustees, either or both of you may write the checks. If neither of you is the trustee, whoever is the trustee pays them on behalf of the trust and with the trust's money,

Similarly, anyone benefitting from the property by living there (or otherwise) should be paying rent to the trust. It is up to the trustee(s) to set and collect the rent, to apply it to the costs and expenses, and when there is a reasonable cash surplus, the trustee may distribute some of the surplus to the beneficiaries.

All this assumes (a) the house hasn't been distributed yet, and (b) typical language in the trust instrument itself. It is very important for the trustee(s) of inherited trust property to read, understand and follow the trustor's instructions.

If the house has been distributed by the trust, things change. In that case, you are likely tenant in common (co-owners) of the house. If so, a question will arise whether your brother's possession and your non-possession of the house is voluntary, on the one hand, versus either the result of an agreement whereby you got something in exchange for giving up your right of co-possession OR because he kicked you out (ousted you), on the other.

If you cheerfully let him live there, he doesn't owe you rent, and if the father-in-law resides there too in exchange for paying some bills, there is probably no net rental income being generated and they owe you nothing. If there is an agreement, and it doesn't sound like there is, the agreement would govern. If you have been ousted, you would be entitled to receive half of the net rental value of the property from your brother.

There are other details, such as how the net proceeds of sale would be distributed, including offsets and adjustments for rents from third parties, payments of taxes, insurance, repairs, etc. if there were a court-ordered sale after a suit for partition, not covered here.