As Laura noted, the pleco and shark are going to be too big for that tank, so it may be easier to rehome them or return them to the store, and only have to worry about the tiger barbs on the move. Plecos in particular are poop machines - depending on his size, that may well be why you have cloudy water. There are also bacteria blooms that occur with new tanks, so that may be what's causing the cloudy water.
If you want to move the fish, I'd recommend having them in a spill proof container; if they are small you can stick them in a gallon jug (maybe 2 gallon jugs since there are several fish) - I've used Arizona tea jugs with success before. That'll keep them secure. I'd stick them in a cooler or insulated bag or something to keep them warm during the move, and keep them in the car with you (where it's warmer than the trunk or truck or whatever else you may be moving with). It will also make it dark which will reduce stress.
Don't open up the bags during transport for the entire 2 days - not until the tank is refilled and you are ready to put them in. In transport, especially with small quantities of water, the ammonia they produce doesn't cause problems while it is sealed, but once there is air exchange the ammonia starts to become toxic. So you don't want to have them in the transport water for more than maybe a half hour once you've opened up the bag/jug.
It is a small enough tank that you should be able to drain all the water from the 10g and leave the gravel moist in the bottom. That should keep some of the bacteria alive during the trip. When you get to the destination, you should be able to just fill it back up, match temps, and add the fish back. Alternatively or in addition, let the filter get a little dirty right before the move and take the dirty filter along in a plastic baggie (to keep it moist). Then plunk that in once the tank is refilled and dechlorinated, to preserve the cycle that way.
Have the tank be one of the last things you break down to move, and one of the first things you set up once you arrive. If you are going to be staying at a hotel or something, another option would be to have the fish all in a 5g bucket (with a lid) and when you are stopped for the night stick a heater in there to keep it warm. You could also put the filter in there depending on the type of filter but it isn't necessary. Actually if you're going to be staying somewhere overnight, bring the fish in regardless of what they're in - even in a cooler bags, you don't want to have them overnight in the car/truck where it will be cold. If they get to room temp temporarily that's fine, although warmer is better.
I've moved fish in a pickle jar, in a mostly drained tank (betta), in a gallon jug, and in a 5g bucket. Never had any losses during a move, although you're going much further than I have. As long as you keep them warm and make the tank a priority when you get where you're going, you should be all set.