I calculated four whole days…..
And caring for a two YO child is a lot of work since they need diaper changing, bathing and almost constant supervision.
And being away from their parents for that length of time may make it hard for them to sleep properly at night.

I would charge your hourly rate while she is awake, then $125-150 when she is asleep.
I would up the overnight rate if she does not sleep through the night.

And yes, for a family member I would charge less.
In most cases.