Maybe you could buy the pulled pork...
(from yourself)
Then it wouldn't really matter where it was cooked right?
I think it would be a great idea. you could pull it and foodsaver it, then on the cart all you need is a hot water bin for reheating the pork in bags, then transfer it to the bin sitting in the hot water (keeps it hot). You could keep the cooled pork in a cooler on ice.
The hot dog cart should already come with the hot water tank/bins on it right?
Then where the condiments usually are you could have bbq sauce.