The other drawback if your telling them the trailer is for something else (like a Geo) if something does happen down the road that ends up causing damage, the insurance that you might have purchased will not cover this deal, you have already broken the contract by towing something else than what was specified.
I do know u'Haul has the larger trailers for like full size cars, i towed a '78 Cadillac Fleetwood from San Diego,CA to Phoenix with a tow bar, they would not let me use the dolly, (was not wide enough) and they were out of the larger trailers that they had mentioned to me. They said that was the only two options for towing the Caddy was with this large trailer, or the tow bar. The tow bar worked great, stuffed up close to the truck, no wiggle waggle at high speeds.
try to find one of those tow bars, it hooks up to your bumper of the towed vehicle, not hard to deal with at all.