It is critical that you iron-out the salary and payment expectations during the negotiations. It sounds as if your expectations are not in alignment with your nanny's. You will need to come to new, agreeable terms with her or find a new nanny.
I had a very successful arrangement with a nanny in which I only paid her for the hours she worked. However, I guaranteed her a set (part-time) schedule per week. If she called in sick, she did not get paid. If I asked her to stay an extra 15min, I paid her for the extra time. She knew upfront that I would not use her during my husband's vacation time, and I gave her almost 2 months notice of when that time would occur, so she could arrange a side job if she wanted. We had discussed all these details upfront and both of us were satisfied. (We also gave her a huge Christmas bonus, as we loved her and wanted to give her a generous gift!)
Your nanny is dependent upon her income -- just as you and I are dependent on our own family's incomes. She has to find a way to pay her rent/mortgage, utilities, food, just like we do. After leaving us, our nanny took a part-time position with a family that offered her "about 20 hours a week" with some varying weeks. Then they ended-up cancelling 60% of that time with a day's notice. Our poor ex-nanny was left struggling to make ends meet and even pay her rent. This is a terrible situation for anyone.
Keep looking for a new nanny that will agree to your terms. Best of luck to you and your family.