If the two dealers have the same corporate finance company, then they just need to execute the agreed-to trade and "swap paper", so to speak. No real need to get a check cut for that, from what I've seen, in the scenario I've mentioned. In some cases, doing the complete "buy" with a company check is the only way some dealers will work, but this can be problematic in some cases. I knew of one dealer that was going to other dealers to get vehicles for their new car customers. They'd take the check to the selling dealer, get the vehicle, sell the vehicle to their customer . . . and then the customer never did get the license plates for their new car. And, as we later learned, the checks bounced after that particular dealer "left town".
Remember, too, that sales at a dealership are dynamic and always moving, usually. There have been times when two salespeople were working deals on the same vehicle. Each customer was promised the vehicle, but it turned out that whoever got their first, got into the finance office first, got the car. The other salesperson had no knowledge that it was "already sold".
If you go into the manufacturer's website and "Build Your ______", once you do that, you can then use that website to link to the vehicle locator website, which will then tell you what other local dealers, or some not-so-local dealers have, in their inventory . . . according to the manufacturer. It'll pull up the window sticker and also give you the VIN. With that information, you can then go to your preferred dealer and let your preferred salesperson then do the search and make the contact with the other dealer. IF you might go to the other dealer during normal business hours, get hooked up with a salesperson, giving them your information, then THEY consider you as a possible buyer, so they might put a hold on the vehicle for a particular period of time, to hold it for you. Or it might be that there are other deals working on that particular car, too, at the other dealership.
So, build your vehicle on the manufacturer's website, check available inventory and window sticker pricing, then go to your preferred dealer and see what kind of deal they'll cut you for the vehicle, plus the additional charge to cover their costs in getting the vehicle from the other dealer. Let THEM do the legwork and such themselves.
With the old GMAC, it was no problem to do a "swap paper" type of dealer trade. No money changed hands, just a call to GMAC to let them know who had which vehicle, in the end. A matter of taking the respective vehicle from one dealer's floorplan to the others. On the Chrysler side, it might not work that way now, though. Hence the need for "purchases" rather than "trades".
Just some thoughts,
CBODY67