Fly. If you can, sell everything and take the cash. You can pick up furniture on freecycle or gumtree. You can get a cheap car. If you do need to ship furniture, get it down to the bare minimum and see if you can get it on the back of someone elses's delivery to save money.

This is one of the most stressful things you can do. Make it as easy for yourself & the kids as you can.