Is it all wheel drive?...Could this be the rear drive unit failing, as they're prone to do?
When the car is taken in for repair be sure the service writer puts down the problem, not just his guess at how to fix it. If the problem is written down but not fixed, don't pay; take a test drive before accepting the car. You didn't get what you asked for. As for the motor mounts---ask for an appointment with the service manager, the boss of the department. Explain what happened, that you paid for something that did not correct your problem, and you want that much credit towards actually fixing what's wrong. Be calm, business-courteous, and firm. Check what auto repair laws your state has and come armed with the law and the facts.
My state lists as one unlawful auto repair practice: "Charging a customer for unnecessary repairs. For purposes of this subsection "unnecessary repairs" means those for which there is no reasonable basis for performing the service." Your motor mount replacement was unnecessary, and in my state unlawful.