Forklift is great for moving trailers - you can put them right where you want them.
I have a device I made - copied from a guy I bought one of my forklifts from; my forklift has 42 inch forks. I have a 42 inch long piece of channel steel that drops onto the top of one of the forks. I boxed the end of it so it can't lift off the tip of the fork and put a loop of 1/2 rebar on the other end which slides under the fork, so it won't tip off with a bunch of cantilever weight.
On the topside of the tip end, I welded a trailer hitch receiver - HF model with a pretty big step plate plus slots for the safety chains. I usually hood a small motorcycle strap through one of the safety chain hooks and run it back to the forklift load apron. I normally leave a 2 inch ball drawbar in it, but I also have a tow hook I can use as a cherry picker and a 2 5/16 ball if I need it.
I can slide it on the fork in about 10 seconds pull the strap tight, and run over and pick up a trailer and maneuver it wherever I want. I often use it to lift heavy objects in "cherry picker" mode. I recently bought a car hauler trailer which was rusty and I used this thing to pick one end of the trailer 6 feet off the ground so I could how rusty it was on the underside - (I did use safety jacks)
That thing is indispensable.