I had a pad poured and retaining wall constructed at my house with this situation. Concrete was cheaper than doing paving stones. I had tried crushed rock over the dirt but this was not effective though it made a good base for the concrete pad when it was added. A third alternative that works well are the ornamental looking cast concrete pieces that are specially designed to allow water to pass through and into the ground.
http://www.concretenetwork.com/concrete/porous_concrete_pavers/
With a Bobcat a person could excavate out the area for the contrete "pavers" in under an hour. Pavers are best bought by the pallet load and not at a retail paving supply. Put sand over the area for maximum drainage and to keep the water running as it now does. What you want to avoid is a solid concrete "catch basin" that funnels water to the side of your house - that would create a big problem that would be expensive to fix.
I would recommend making the area for the trailer at least 2 feet wider on the sides and at long enough that your tow vehicle's wheels and the trailers wheels are never on the grass.