I concur with Toaster...
Last time I checked with a rental place, they wouldn't let you tow with their vehicles unless the trailer was theirs too, and THEY hitched it up.
Remember though, that you can get a used van or pickup very reasonably in good condition if you do your homework and shop hard. You don't have to spend a fortune for an occasional-use tow vehicle. A high-mileage truck or van that has been well maintained and is in good condition may be just the ticket for towing for the occasional nearby weekend getaway. You'd be amazed at what's out there for under $10k in this world of new $30-$50k trucks and SUVs.
Full-size vans are probably the best buy as they can be found in like-new condition for very little money.
AIR 2053 Current: 2006 Born Free 32 RQ Kodiak Chassis, & 1995 Coachmen B-van
Former Airstreams: 1953 Flying Cloud, 1957 Overlander, 1961 Bambi, 1970 Safari Special, 1978 Argosy Minuet, 1985 325 Moho, 1994 Limited 34' Two-door, 1994 B190 "B-Van"