Stressed and moving

I cleared everything out of one room and set it up as a playroom for the day. I put the TV/DVD player in the room and a couple of favourite toys and packed lunch/snacks. It kept them so busy and safe out of the way of the lifting and carrying etc.
All the stuff in the room easily packed up in the car to be unpacked at the other place (I put it in my room as setting up my room could be done once the kids were in bed).
Otherwise have you thought about paying a teenager to keep an eye on them in one room for the day? It's not like you wouldn't be there.