Must I serve my mother-in-law, who is sick and bedridden, despite her having other children and my being responsible for my own sick and young children?

The wife is not obligated to serve her husband's mother, but if she volunteers to do so, it is an act of kindness. Serving and caring for the husband's mother is an obligation upon all of her capable children, either by themselves or by hiring someone to do it. The husband should communicate with his wife and explain to her that her service to his mother is not obligatory upon her, and that he and his siblings are responsible for serving her, or for hiring a maid for her, or for moving her to one of her children who is able to serve her.