After someone dies and they still had a house and assets, what’s the very next step after the funeral?

You will need to get copies of the death certificate. Notify anyplace they are currently getting an income from and provide them with a copy of the death certificate. Notify the financial institutions they use. Consult with an attorney but since the will states you and your brother are to execute the estate you should be able to handle most of it. I had the same situation I was in charge of the settling of the estate even though I had a brother it was me alone. Be patient, it takes time to get things settled. It took me about 15 - 16 months to get everything settled. I hope you have the authority to write checks on their checking accounts because that will save you a lot of time and money.