Can't imagine a lab sitting on two small kids for a length of time.
You can rig a dog crate onto any small trailer, the trailer would also provide additional storage.
Can't think of any other options because the dog doesn't have opposable thumbs.
But, you do!
Just stand on the running board, hang on and teach the dog how to drive!!
You'd be right there to yell at 'em if he does screw up.