L.M.
J.,
I've been lucky enough to have a nanny in my home during from Tues thru Fri (my husband is off on Mondays). I pay her every week, even if she only works one day. However, I do not pay her when were on vacation, as long as I've informed her in advance that her services would not be needed.
When my nanny was out of the country for a few months, I used an after school program. Their policy was; I had to pay a full week in advance, if I was going to use them for even one day. I also had to pick my children up by a certain time, or I would be charged for the additional time.
Actually, the terms should have been established before you engaged her services. I would politely ask her if it was possible for you to drop off your child at 7:15, explaining that you're getting to work late. However, if she indicates that it's not possible or difficult, politely say "ok, thank you". As you know, it's very difficult to find quality day care at an affordable price.