Op here. I actually currently pay 20, which is on the high end for one kid.
Yikes, you are already overpaying but you are in a situation of your own making and still need to raise her rate for a second child. Go with the standard rate of $1/hr and apply that for all hours. Yes, you are still overpaying for when your child is in preschool, but if you have a good nanny, and you want to keep her, this is likely the best way.
Parents really need to consider carefully the rates for their jobs and plan accordingly so they have room for annual raises. The market in DC is $15/hr for one child. If you offer $19/hr, you will price yourself out sooner than later.
Of course, you can pay what you want, but overpaying isn't smart if it means you need to look for a new nanny every few years.