Is it obligatory for the questioner to return permanently to Egypt to satisfy his mother, knowing that he is settled in his work abroad and his mother lives with his married brother?

There is no blame upon you for continuing to work outside your country as long as it does not lead to neglecting your mother or falling short in a duty that is obligatory upon you. Nevertheless, if your return would not harm you, then it is more virtuous to return to please your mother, for your proximity to her will help you fulfill your duty to her and show kindness to her, and showing filial piety to one's mother is one of the best acts of drawing closer to Allah.