Must I obey my elderly, unconscious mother when she refuses help with her personal hygiene, knowing that she curses and invokes against me and my children when forced?

As long as you are doing what is in your mother's best interest and treating her with as much gentleness as you can, there is no sin upon you for compelling her to purify herself and maintain necessary hygiene. Rather, you will be rewarded for it. Your mother's supplication against you and your children will not harm you as long as it is without justification. Our advice to you is to strive to be gentle with her, patient with her, and kind to her to the best of your ability. Rejoice in the blessings of this righteousness in this world and the hereafter, for honoring one's mother is one of the most beloved deeds to Allah and the quickest in reward, and the most hopeful for blessings in sustenance and lifespan. Indeed, Ibn Abbas said: "I do not know of any deed closer to Allah Almighty than honoring one's mother."