I will give the "selling" dealer the 1st chance at service. One of the reasons I chose to buy the car there is because of the reputation of the service department. If they will not do an adequate job, then I will find another dealer to do the work. So far, that has not been the case.
If another Chrysler dealer would ever refuse to honor the warranty, I would be on the phone to a regional D/C rep, followed up with a formal complaint in writing.
In my opinion, once the dealer has been paid for the vehicle, that transaction is complete - The service department is a completely separate part of the dealership.