If you are going to carry several barrels then as others have said, strap them in with a good heavy duty ratchet strap or straps.
But also have some very heavy duty bungees wrapped a couple of times through the anchor points.
If you have this done you can slide the ratchet straps through the hoops of the bungees, this allows some elasticity to take up any slack as you pull the rachets tight.
You may not think you would have any slack of course, but it does make a difference and helps to keep things from working loose.
But far better to have a tank in your vehicle and a submersible pump, I got my sub pump from Gardiners, but most of the suppliers do them, mine fills a 25l barrel in less than a minute.
As said, easy enough to power the pump, just have an old car battery to run it off.
I may be fully van mounted, but I also have a backpack converted into a trolley, and this is used constantly.
Used in conjunction with the full van mount it works perfectly, they really complement each other.
A van tank is far more secure than a load of barrels, if you only wish to work with a trolley then you need only carry one or two barrels in the van with you.
You can then drop a full one off for instance if you are on a big job, just leave it somewhere half way around the job (we do this on a couple of jobs).
Ian