Hi,
Moving is a pain but it can be done. This is what I did and I lost nothing in the move.
Sand will take about two hours of not disturbing it at all for it to settle. Putting in water, moving rock, anything at all, and it stirs it up all over again.
The best thing you can do is set up your tank at least a couple of days before the move. I actually purchased another tank and bought new sand. I set up the water with a heater and power head running in the new tank. THEN made my move.
Rock was placed in a new plastic garbage can I purchased for the move. My Royal Gramma was hiding in one of the rocks and I didn't know it. I don't know how but she made it!
When I actually moved I took all the sand I could and put that in first. I put my rock in, not set up like I like it but in there enough to let my fish back in ASAP. I moved in cold weather so time was not on my side.
I put everything alive in gallon baggies to move, and acclimated them to the new place just like when I buy from the LFS.
If you have no other choice:
As long as the lights are off and the water warm and aerated (use an air stone) the coral will sleep and be alright for at least a day in the tubs if you have to.
Your fish as well, but be careful, cramped quarters causes problems. Use your established tank water at first and every 10 hours change the water 20% (make sure it is the same temp. and salt) use an air stone for the fish tub a power head to too strong for it, and will churn the water too much.
You could maybe put a couple of rocks in the tub, it will help to give the fish a hiding place and offer a surface to breed good bacteria. One of those little bubble corner filters might help a little. I haven't seen one of those in a while though.
Be sure to remove the rock for the move because it will shift and might crush a critter.
If you can save your old water in jugs... and put it into the tank before reintroducing the inhabitants, it will help a great deal.
Good Luck