Pushing the dolly under the wheels isn't the right way to do it, but if there's no way to drive/roll the vehicle onto the dolly, it can work. I'd suggest having someone else IN the vehicle to control it just in case anything happens, though. You might want to chock the rear wheels AND have the parking brake applied as well. I'd say put the transmission in neutral instead of in park while doing it, too.
Mark the orientation (tire crayon or paint works good), then disconnect the rear driveshaft at the rear differential before towing. Just disconnecting it from the transfer case still lets it turn with the driveshaft flailing around under the vehicle at speed.
A car hauler trailer is optimal for towing, but a dolly lets you get away with towing one Explorer with another. Keep the speed down and take it easy and it should be okay, especially if it's a short drive.
