You should be okay as long as you avoid sharp turns. It looks like its intended for 1/2-ton pickups. Your minivan won't have as much clearance to the fenders as a pickup (due to ride height), but that only matters when making turns.
That said.... Having to constantly worry about turning too sharp could really make for a stressful driving experience. I even get nervous about fender clearance towing my Fiesta, and its has almost 4" of clearance to the fenders. Still looks awfully close when making sharp turns though!
BTW - Have you considered a Transit Connect? It's only 72.2" overall width, and weighs much less than the traditional minivans.
