Hey Plath,
Been away all week, wish I would have been here to give you some support!
Can they shop some other time than naptime?
When are kids were little we were pretty loose with them except in two areas naptime and bedtime, they needed that routine and we were very vigilant about it.
What is your BIL doing through all this, is he working, or is he dumping her on his mom and she is passing her on to you?
Can you all work out a schedule for trips to the market and such.