Nanny pay?

Hi everyone! I could use some advice from fellow nannies.

My nanny family is going out of town for 10 days, and I’ll be staying at their house with one baby and one 5 year old the entire time. My regular rate is $30/hour, and I do not receive overtime pay.
(I know… I’m looking for a new job.)

My thought was to charge my regular hourly rate for all working hours each day (for example, 7 a.m.–9 p.m.) and then charge a flat overnight fee of 120 instead of hourly while everyone is sleeping.

For those of you who have done extended overnight care, how would you structure the pay? What would you charge for the overnight fee? I’d love to hear what has worked for you. My nanny mom has tried to cheap me out the past few trips and has been throwing “we can’t pay you this” after buying me plane tickets for travel. Just trying to protect myself.