Are you only going to be watching out for the kids, or will you be in charge of managing the household during those 3 weeks? IOW, are you truly the de facto parent and homeowner, or is there someone else who will be available to help take care of things if the dishwasher floods the place, or one of the kids gets ill at 3 am?
Is this happening when the kids will be in school or out of school?
What sort of school activities/outside activities will the kids be doing?
If you are sole charge, don't accept less than 3K a week, especially if you and the kids don't know each other well - the limit testing will be draining.
If you will have someone "on-call" to help in case of emergency, I would say anything from 1,500 - 2,000/week is reasonable.
I'm presuming here that you are in a major metro area, and not a small town.