Most places don't pay you for time when you are allowed to sleep. I have worked in 2 states in care giving situations like child care and when they went to bed I went off the clock.
I called the labor board in one state to find out if that was legal, I feel like that if I am off the clock I am able to leave, go out and do stuff, etc...that I am "off the clock" but the state told me that laws are different for caregivers, they are there but not on the clock if the charges are not awake and therefore, even if they can't leave the premises, they are in fact not working and can be considered to be off the clock.
I think being fair and asking the mom what her idea is before even thinking about it, she may have a very low figure in her head and then you'd say a huge number. Or she might have this huge number and then you'd say one a lot less...
When I was a nanny and the parents had to go to an out of state funeral, one of their mom's died, I had all 7 kids for a long weekend. They left over $100 just for food and everything else was fully stocked. I had access to an account for an emergency if I needed it but I was under strict instructions that emergency room visits that required medications or some other emergency was the ONLY way it was to be touched. I had the mechanics number, the repairman, and in reality would need nothing else.