Rental Trucks do not have electric brake controls and RV plugs for trailer wiring so I doubt you will find a Rental Company that would permit you to tow a private trailer.
Arnie
2003 Travel Supreme MH
38KSO1 Cummins ISC 350HP
Car Dolly w/1996 Toyota RAV4 2WD
1963 Pontiac Grand Prix
Outside of the heavy equipment rentals, the only other option is usually full-size vans from smaller outfits. Enterprise says no. But many other places allow it with their full size Ford vans (Chevy rarely because Factory tow package is less complete). Triangle and Adventure vans are a couple outfits that allow it, and come equipped with Class 4 tow packages. I'm not sure about brake controllers though, but the E350s are plug-n-play so it's easy to add your own.
Bryan
2000 Ford E350 DRW Wagon (14-pass all captains chairs)
V10 w/ Banks PowerPack, Diablo Predator, 4.56 LS, 230,000+ miles
Had: Weekend Warrior 41' FSW (still looking for its replacement)