Is my mother sinful for not serving her elderly and incapacitated mother, despite her mother appreciating that and not being bothered by it, and her need to work to provide for her children, while the grandmother has enough to hire a maid?

If a grandmother has sufficient money to cover her expenses and afford a maid, then her children are not obligated to spend on her or leave their work to care for her. The duty of financial support and care for her falls upon all her children according to their ability, if she is in need. It is obligatory for the father to visit her, inquire about her well-being, and assist her, for honoring one's parents is among the greatest acts of drawing closer to Allah.