A.C.
I don't think I really need to tell you that you should have figured this all out before she started working for you. It is quite possible that she is taking advantage of the situation--but you have created the situation.
Hard feelings? She is in your employ. While those who take care of our children tend to become part of the family, as the employer, it is up to you to maintain a professional relationship.
If she is claiming to have been hurt on the job, you can justifiably request that her doctor write the "rest" order or require that she get a second opinion (at your expense).
If you like and trust this nanny, that is priceless and you should pay her for this time off. That being said, you should use her "annual review" to define her contract.
As a single mom, I don't have the option of staying home. But I also have an agreement with the daycare. Just because I don't define their policies doesn't mean I don't make sure they are following them.