From the CBR, can I rent a van for a day?

Not directly from there but you can from the car care center or from either the Swan or Dolphin. (Cant remember which one.) From what I recall, you may be able to get a shuttle to/from the Car Care Center. Others may be able to confirm that.

ETA: I think the company that runs the rentals is Enterprise. (Again, someone can/will confirm.) If that is the case, you may be able to check with them to see if they have the car/van style that you need.

Alamo/National, not Enterprise.