Yep; I would give her 75 hours of PTO. If she can use all three weeks however she wants, and you're also guaranteeing hours for the weeks you're away but she's available to work, then I wouldn't give any sick leave. I would just call it all "paid time off" to use as needed.
With our PT nanny, we only did two weeks of vacation, but made it all "her choice." I also told her she had to use it in 5-hour blocks (she also works 5-hour shifts). For other come-in-late/leave-early requests, we work it out case-by-case. Either it's unpaid, or she can make up the hour or two some other time.
I would strongly encourage you not to give all three weeks up fron but to have it accrue over some period of time. It can be hard to keep PT nannies just because a lot of part timers are only doing it for a reason (another PT job, own business, kids in school) and move on more frequently than full-timers. Each time you hire someone new, if you give all the vacation up front, you'll be obligated to pay out 3 weeks of PTO to the departing nanny even if she hasn't been there long, and 3 weeks is a lot. Just something to consider. Maybe she earns x days per month, or one week after two months and all three after 6 or 8 or something like that.