Is it permissible for a father to leave the family home and reside with his son, and what is the ruling on the son accepting him?

There is no blame on the father for leaving the house and residing wherever he wishes. He is obligated to provide for his wife and young children according to what is customary, to fulfill his wife's rights, to keep her chaste, and to spend nights with her to an extent that removes the desolation of loneliness from her.

If the father asks his son to allow him to reside in his house, there is no blame on the son for responding to him, nor is there any sin on him for doing so, even if the father is neglectful of his wife's and children's rights; for his neglect is not a consequence of the son housing him. Moreover, his fulfillment of his duty is not contingent on his residing with them. In this situation, the right belongs to his wife to demand it if she wishes.