The parking brake is only connected to the rear wheels and it not tied to the hydraulic system, so the shaking in the steering wheel is not really a sign that the parking brake was left on.... Does your Caravan have rear drum or disk brakes? What model year is it?
Since you didn't have any problems getting the van up to highway speeds it sounds like either the parking brake was not fully engaged or it's not adjusted properly. But if it was making contact at all you can expect some very worn parking brake pads/shoes and possibly warped drums/rotors/parking brake drums. If the parking brake assembly on your van is built in to the brake caliper you may have heated the brake caliper sufficiently to damage the slide pin grease to where you want to have the pins cleaned and greased. It also sounds like you may want to consider connecting a beeper to the brake light circuit as well.... Seems odd that Chrysler didn't add this feature to the BCM. Heck, they beep if the turn signal is left on, wouldn't it make sense to have it also beep if the vehicle is shifted from Park with the parking brake still engaged!?!
-Rod