Is it permissible to pay the water bill for a building inhabited by the poor from zakat funds, knowing that my mother paid her share, but the remaining residents, some refuse and some are unable to pay?

If the families are poor, then they are eligible to receive zakat, and you must give it to them and enable them to possess it. They have the right to dispose of it as they wish. You should not pay their bills with it unless they ask you to do so after they have taken possession of it, because zakat is the property of the poor.