Make sure that the kids have a packed bag with an extra set of clothes, toiletries and toys. Having your boxes labeled to the specific room they belong makes for faster moving and unpacking. Packing each room one at a time is the best orderly thing to do. Also pack up room that you use less often first, a good starting point is the guest room or formal areas of your home.
Labeling boxes clearly helps the movers know where to take boxes for you. If its possible have one parent keep an eye on the kids while the other deals with managing the move. The key to a successful move is proper managing. Know beforehand where you want to place couches, TVs dressers etc. This way there is no time wasted pondering where you want to put things. You also don't have to ask movers to move things several items. If it helps sketch out your floor plan for your new place and place your furniture in each room there are also tools online that can do this for you as well. Planning ahead and over-planning is never a bad thing. Remember try and keep thing you can control under order.