Is it obligatory for a son to fulfill his promise to his bedridden mother and his sister to accompany them for 'Umrah next Ramadan, and to forgo the opportunity for Hajj that he and his wife won, knowing that he has not yet performed the obligatory Hajj (Hajjat al-Islam)?

If he is able to travel with his mother for Umrah before Hajj, he must accompany her as an act of filial piety. Otherwise, he should perform Hajj for himself first, because Hajj is an immediate obligation upon him. If he cannot reconcile the two, he should explain the situation to his mother. If it is possible for his brother to travel with them, he should help him. If no mahram is available, a woman is permitted to travel for an obligatory Umrah or Hajj with a safe company; otherwise, she is not.