Can you start with her looking after the kids at your place? Explain that your parents have everything for the kids at their place and you know that she doesn't so it would be easier to start with her coming ovber to look after them at your place.

Plan in advance to go out for dinner or something close by with your DH and go out for a couple of hours. Gradually build it up and in a few months you might feel more comfortable leaving the kids at your IL's place once they have proved themselves on your turf.