my mom disinherited by brother but they have recently reconciled. How does she go about reinstating him back into the will?

Does she only have a will? Or a trust and a pour-over will? It's important to be sure she knows which she has. Whatever document(s) disinherit your brother should be legally amended, with all proper signatures/witnesses/notary stamps as required. Or a completely new will (and trust, if needed) can prepared. This might be a good time for her to review all her documents, and be sure all the people she has named, both to receive property, and to act as her agents, are still the ones she wants now.