That would be fine if properly structured. There are tax and other employment law issues as well as possible Medicaid implications if your mother-in-law requires nursing home care in the future. The arrangement should be formalized in an employment agreement so that there are no misunderstandings down the road.
Your sister will need to report the compensation on her tax return. If the care is ordered by a physician, your mother-in-law should be able to deduct the pay as a health care expense. Given all of these issues, I’d recommend consulting with an elder law attorney or accountant (or both) before moving ahead.
To read more about caregiver contracts, refer to this article.