Who has a greater right to an 'Umrah, the mother, the father, or the wife, if the husband only possesses enough money for one person's expenses, and both parents are unable to perform the obligatory acts? Also, why is the husband not obligated to travel with his wife if he has enough money for her journey, even though Hajj is obligatory for her?

It is not obligatory for a son to perform Hajj on behalf of his parents at his own expense, nor for a husband to perform Hajj on behalf of his wife, even though doing so is considered an act of righteousness and good companionship. When rights conflict, the mother's right takes precedence, then the father's, then the wife's. Hajj is not obligatory for a woman unless she has the financial capability.