Start paying her. If you can afford it, compensating a family member gives you more power in setting expectations, say experts.
Use your pediatrician's authority. "Kaylee's doctor says we must put her to sleep on her back" is more effective than explaining the SIDS risk on your own.
Be direct about why this matters. Joking about disagreements isn't going to help. Say clearly what you'd like to see happen.
Let her go, if necessary. Don't keep your child with a relative just to avoid awkwardness. You can always say, "Our doctor says Jacob would benefit from being around other kids, so we're going to start going to a daycare."