Is it permissible for a father to take money from his children who provide for their mother and sister, while he does not provide for them, and given that their mother dislikes him and he has uttered a divorce oath against her?

The father must provide for his poor children who are unable to earn a living, but he is not obligated to provide for his well-off children. The wife has the right to maintenance from her husband unless she is defiant (nashiz). If the husband refuses to provide maintenance, she can refer the matter to a Sharia judge. If the divorce is revocable, the wife is still considered a wife, entitled to maintenance and housing, and she must obey him in what is good. However, if her waiting period (iddah) has expired or the divorce is irrevocable, she is no longer bound to him, and he is not obligated to provide for her maintenance or housing. If the mother does not have enough to sustain herself, her maintenance is obligatory upon her well-off children. If the father is in need, his well-off children are obligated to provide for him kindly. If he is not in need, they are not obligated to anything unless they voluntarily contribute. Honoring the father and accompanying him with kindness is obligatory, no matter how much he may have mistreated or fallen short.