The problem I see is that this is a related party transaction. By selling the home to the LLC, you are getting a free step-up in basis, which will allow you to claim a larger depreciation deduction. If you were simply to start renting the home, you'd have no step up in basis & lower depreciation.
I suspect that the IRS regulations will require that you maintain your basis for your 1/3 interest, while your brother & dad get a step-up in basis to 1/3 of FMV. The answer may depend on whether your LLC is taxed as a partnership or corporation. I strongly suggest you consult an enrolled agent or tax attorney & get a formal opinion. Be sure the person you hire has malpractice insurance in case they're wrong.