Is a wife required to serve her mother-in-law who is healthy, wealthy, and treats her poorly, and if she refuses, is she considered to have transgressed the limits of Allah, especially with the husband forcing her to please his mother?

The default in Muslim interactions is affection, cooperation, and compassion. These values are emphasized with marriage into a family, so your honoring of your husband's mother is an honoring of your husband, and her honoring of you is an honoring of her son. Legally, you are not obliged to help your mother-in-law or serve her, and neither your husband nor your mother-in-law has the right to compel you or harm you if you do not do so. It is wise to placate her and guard against her harm, and a maid can be provided. A wife is not legally obliged to live with her husband's relatives, and it is your right to request an independent dwelling, and your husband must provide it.