Actually, a flat rate for overnights is fairly common all over the US. A quick google search can confirm this.
http://www.breedlove.com/answers/Overnight-Nanny (Breedlove's advice on the law)
http://wishuponananny.com/faq/ (an agency in Chicago)
http://www.ggmg.org/recommends/NannyPay.html#Overnight (a parents group in CA)
http://www.ehow.com/decision_7218524_much-should-pay-overnight-nanny_.html
http://parents.berkeley.edu/advice/childcare/nanny/overnight.html (results of a survey of parents in Berkeley, CA. Interesting because there are many options from flat rates to full hourly and more)
http://www.mamapedia.com/article/overnight-pay-for-part-dash-time-nanny (a variety of responses from all over the country)
http://www.parkslopeparents.com/docs/NannySurvey2011.FINAL.pdf (This is an interesting overall survey from 2011 about nanny pay and policies. While it includes overnight pay, it is actually far more informative on many aspects of nanny employment and could help nannies in their negotiations.)
I'm not saying that a flat rate is automatic. There are many different opinions on this. For me, it would depend on the age of the charge. If a child likely to wake (babies, toddlers and some young elementary students) then I think it is fair to pay the nanny her regular rate. However, OP's children are significantly older and the nanny is very likely to be able to sleep through the night. In that case, she should be compensated for being present and on call, but since she is not expected to perform any duties because she is sleeping, a flat rate is appropriate. Of course, if a child becomes sick and the nanny has to attend when she would be sleeping, her regular rate should kick in. That's only fair.