Babysitting when kids are sick?

Hi all!

I have a bit of a predicament and am wondering if anyone can help. I have a nine month old daughter, but occasionally babysit my niece (1.5) and two nephews (4 and 6). I just bring my daughter along. I am supposed to babysit tomorrow, but my nephews are sick and I really don’t want my daughter sick for thanksgiving! I’ve tried to tell my sister that I don’t want to babysit, but she is getting very upset- hostile even! She claims that no one else can babysit although she won’t ask anyone. I feel bad cancelling a day in advance but don’t know what else to do. I have babysat before when they are sick and my daughter has caught what they have both times. Should I babysit anyway or do I have a right to cancel?

Thank you in advance!