Changing out the lower motor mount/ transmission mount....

You'll have to disconnect all the motor and transmission mounts before you can raise the engine.

Watch the video, it tells you everything you need to know. How to replace Motor Mount or Transmission Mount

The exact location varies depending on model, engine size, power and suchlike.

Most models have three mountings and there are no lower ones, though there could be a steady bar or torque reaction mount attached to the bottom of the transmission.

The power unit tends to be mounted with one mount high up on the extreme right and two on the transmission end, one at the back and one at the front.

Use a floor jack or trolley jack under the transmission. Also use a block of wood if you have the jack on the transmission's lower pan. You will see that the whole engine and transaxle assembly will tilt down somewhat with the transmission mount removed. If it is not enough to replace the sensors, raise the jack back up and take off that dogbone, then lower the whole thing again until you can get to the sensors. Be careful when getting the mounts back on, that the engine and transaxle settle down perfectly into the mounts, so you have no vibration issues.

Indeed the engine mounts can cause this type of symptom, have a local shop check the engine for excessive lift up on gear engagement.

Lower engine in bay, loosely attach motor mounts. Install transmission, mate to motor. Install transmission mounts, tighten motor mounts.
Hook up wiring and hoses. Fill all fluids. Reinstall driveline, hook up exhaust and linkage. Reinstall hood. Test work, check timing and carb settings.

There are 2 of them, one on each side of the motor. They are located at the base of the motor about center and connect to the front cross member. If you have a sideways mounted 4 cylinder you may have 3 motor mounts, this is common with some Dodge vehicle, They are located 2, upper and lower, on the passenger side of the motor and one actually on the transmission side that connects to the transmission.

passenger side, under exhasut pipe, against motor, close to tranni.

There are four total mounts.

1. Upper engine mount located on the passenger side of the engine. Get this at the dealer, aftermarket, especially Anchor brand are garbage.

2. Lower engine mount, often refered to as a "dog bone" mount because of its shape. This one is located on the lower passenger side. You'll have to remove some splash shields to get to it. Aftermarket is OK.

3. Upper transmission mount, also refered to as a "dog bone" mount. Located under the battery.Aftermarket is OK.

4. Lower transmission mount. Located under the transmission. As with the top engine mount, dealer is better quality.

The two dogbone mounts usualy last a very long time, its the others that fail over time. Especially the upper one.