Q: Car shaking and sputtering when idling and driving

The information provided leads me to believe that your Lincoln may be experiencing a lack of fuel pressure to the engine. If the fuel pump is unable to provide the specified fuel pressure to the engine properly, then symptoms like you are experiencing with your vehicle can occur. The information you have provided is a bit limited, however if these symptoms occurred immediately after having your transmission replaced, it is possible the two are indeed related. To be 100% certain however, I highly recommend enlisting the assistance of a certified mechanic to come by and inspect your Navigator. They will have the knowledge and tools necessary to determine if a previous repair is related to the issues your Lincoln is having as well as identify the root cause of your Navigators shaking and other symptoms. They will also be able to assist in making the repairs necessary to get your Lincoln accelerating and shifting smooth like a luxury vehicle should.