Q: Transmission and possibly engine problem - 2011 Toyota Yaris

The vibration and jumping may be caused by a broken engine mount. Very often a failed engine mount will cause excessive movement and bump against the stops. An easy way to see this is to have the parking brake held and the vehicle in gear and blip the throttle while someone watches the engine from a safe distance. If there is a broken mount, you will see the engine seem to jump or lunge inside the engine bay. Consider hiring an experienced technician like one from YourMechanic who can come out and take a closer look at what’s causing the noise and offer a more personal diagnosis.