Is spending from the deceased husband's money and the mother's private money on the children considered Islamically permissible or forbidden?

The guardian of an orphan must preserve and invest their money for their benefit. It is forbidden for the guardian to consume it, except for the poor and needy, in a reasonable manner, as Allah Almighty says: "And whoever is rich, let him abstain; and whoever is poor, let him eat in a reasonable manner." As for consuming it unjustly, it is a grave and destructive sin, as Allah Almighty says: "And do not consume their properties with your properties, for indeed, that is a great sin." The orphan's money should only be managed in the best possible way, such as for food, clothing, and education, provided there is moderation without extravagance or stinginess, with the possibility of saving a portion of it for the future.