Out of kindness and a sense of goodness she should. From an Islamic POV he is responsible for his parents and she for hers.
If the parents are young enough to have young children, then most likely they are not in need of physical care. If they are old and infirm, then she should absolutely help care for them. However, that doesn't mean that she should be treated as a glorified servant.
The real question is this: Is a husband liable to take care of his in-laws?