Is it permissible for the mother to spend the money sent by the daughter's father on household needs, or should this money be limited to the daughter's needs only, knowing that the current husband fulfills all of the daughter's needs?

The daughter's maintenance is obligatory upon her father. If the husband is unaware of the money her father sends her, he must be informed. If the husband agrees to continue providing for her, the money should be kept for the daughter until she reaches the age of maturity, at which point it is given to her, as Allah Almighty says: "And if you perceive in them sound judgment, then release to them their property." If the husband stops providing, then the mother should spend from that money on the daughter.