Many providers DO get paid vacation/illness days. You need to see what the contract YOU signed says and honor that. If she is using paid days alloted to her in the contract YOU agreed to, and you do not honor it, what does that say about you?
As a provider, I used to get 20 PTO days, plus paid holidays per year. After so many years in the industry, I felt I deserved it and my local market could bear it. Most of my clients got similar, so I did too.
When the economy went in the crapper a few years ago, I upped my prices to absord that 20 PTO days, and now get unpaid vacation and illness days (but still get 9 paid Holidays). It is to my advantage to close a limited amount of days per year, but my amount is not limited. Since I have done this I have taken somewhere between 8-12 a year, and am fortunate to have access to a (high priced) sub who can come for chunks of time so I can get to Dr appts, etc. I used to have to close full days to make an all day run of attending dr and dental appointments, etc. Its the only way many of us can get such things done.
How different would your situation be in a Center based childcare? Around here, from my understanding, parents are usually alloted a week (5 days) per year to take out of childcare and not pay. You WOULD have childcare more consistently if one of their employees were to be ill or have surgery, etc. But you pay for that. How much more would your daycare bill be for the year? Its a give and take in different care situations and home providers are allowed to have PAID days off, as long as it is within the contract YOU signed.
Best of luck!