Is it permissible, Islamically, for a father to dispose of the money of his two daughters whose mother has passed away, without their consent, given that they are adult and of sound mind and in need of the money? And would he be sinful for doing so?

The mature, sane heir—whether male or female—has the right to claim their share of the inheritance, and the father or anyone else is not permitted to prevent them from disposing of it. The father must fear Allah and give his two daughters their right from their mother's inheritance. He is not allowed to place an interdiction on them as long as they are mature and sane. They, in turn, should advise their father gently and respectfully, explaining the Sharia (definition) ruling to him, and that placing an interdiction on an extravagant heir must be done through a judge.