What is the solution that would please Allah the Almighty regarding the problem of a father who wishes to marry, but his daughters refuse, demanding that their brother host their father in his rented apartment, which his wife rejects, while the son aims to please his father?

Sisters do not have the right to object to their father's marriage; rather, it is an act of filial piety to assist him in it. Some scholars have even gone so far as to say that it is obligatory for children to marry off their father if he needs it to maintain his chastity. You must provide him with suitable housing if he does not have it, and your wife has no right to object to this. However, if the father changes his mind about marrying, then it is obligatory for you to care for and serve him.