I think buckets with lids will leak less. I did rubbermaids from Ft. Collins to Loveland in the bed of my pickup and when I pulled in it looked like I had sprung a leak! Screw on lids are even better IMO. For a 4 hour drive I don't think you need to fuss with heater and air pump. Think of fish being shipped via FedEx Overnight....they are in baggies for 10-12+ hours and somehow they make it.
Would it be possible to have a tank set up at your new location? That might be good, so at least you have good water up to temp and ready to go so your fish can relax after the stress.