Is a visit to one's mother obligatory, given the ability to pay a large sum of money, the presence of legitimate impediments in the mother's country, and the difficulty of the elderly mother traveling?

If a mother asks her son, who is able to travel, to visit her, then it is obligatory for him to do so. However, if he is unable or if she is content with him staying, then he is permitted not to travel, as long as he continues to honor and maintain ties with her through available means. For honoring one's mother is among the most beloved deeds to Allah and the most blessed.