Yes it is called blended rate overtime ...

OP here-- many thanks! really appreciate it!

Strictly legally speaking, the OT rate is based on a weighted average rate of the work week. So of 50% of the time it is a rate of $10/hr and 50% $20/hr, the OT rate would be 1.5 x 15$/hr.

Just be sure to show the nanny the math explicitly whether you decide to do this route or simply paying OT on the higher rate, so there is no confusion.

The relevant law is linked below.

See bottom paragraph on first page

http://www.dol.gov/whd/regs/compliance/whdfs23.pdf

Not sure what the legal answer is, but I'd expect to be paid OT at the share rate. What you pay for the share OT is probably less than her single child rate, and if it were just your kid you'd be paying more, so its still a deal.

Our nanny will be sitting for our toddler solo for 6 hours each day (morning to mid afternoon) and then, when school gets out, she will sit for our child and a school-aged child until we get home from work (6:00 or so).
For the first 6 hours, she will receive her one-child rate from us.
For the shared time in the afternoon, she would get the two-child rate (slightly lower) from us (and, of course, a coordinating two-child hourly rate from the other family).
The total hours in the day will exceed 8 hours and the total hours for the week will exceed 40. So, she should be paid at time and a half for her overtime hours.
But which rate do we use?
There is a view that says, well, the overtime 'happens' at the end of the day, so it would be time and half on the lower two-child rate.
But I am not sure that is right.
Then again, I tend to be my own worst enemy with these things and end up paying more than I later learned I should have in many instances.
We definitely want to pay the fair amount to her. I'd welcome thoughts on which rate people think is appropriate.
Thanks!