For us, stability means staying together; keeping the children's favorite items with us, such as: books and toys and anything that goes to bed with them at night; and making the new house look as mch like the old as possible. The best way to do this is to make sure the first thing I do when we move in is put up pictures and get the children's bedrooms and playroom and kitchen in order.
Once the children have their living spaces in order, they can start to adjust and settle in to their new surroundings. All the other unpacking can come later. If the children are happy in their home, they can play and relax and you will have time to unpack everything else.
My number one piece of advice during a move is to pack tools, lamps, cleaning supplies and bedding, and other linens, in boxes that will be easiest to find and the first to be unloaded.
More to come...