You need to do some "engineering"...
I had similar questions about the ability of my TDIs to tow. Typical loads have been up to 600 pound motorcycles, 800 pound motorcycle with sidecar, and 1200 pound loads of wood pellets for the biomass stove. Most of these were hauled on a 300 pound 4' by 8' trailer, and occasionally with a 650 pound 6' by 12' trailer. My 2003 Golf TDI with Curt hitch handled all these loads with ease.
The challenge came when I decided to acquire a small diesel tractor. The lightest tractors with the features I needed (3 point hitch and a loader) weight around 1300-1400 pounds stripped of implements. Mt first 4 by 8 trailer, a "Carry On" from Tractor Supply, proved rather flimsy so I bought a beefier 4 by 8 rated for 2000 pounds gross weight. It's a simple frame, suspension, axle, wheels, and lights with no floor and sells for around $400-450 at midwest farm stores like Fleet Farm and Farm and Fleet. Even after I added a 3/4" thick plywood floor it barely weights 300 pounds. Dealer delivered the tractor for me so I haven't actually had to haul it anywhere, but I did a test load and tow and it worked fine- It's right on the TDI's 750 kilo limit for unbraked trailers and well within the hitches 200 pound tongue weight/2000 pound total weight limit.
So what you need to do is find an ATV and trailer that do what you need but are within your TDIs towing capacity, which for all practical purposes is 2000 pounds total weight. Remember to add on everything you'll have attached to the ATV, and keep in mind that a couple heavy passengers in the back seat may cut into your allowable tongue weight and thus total trailer and load weight too.
Get out the ATV and trailer brochures and have at it!