Car shaking while moving slowly or stop

What is the idling speed? Most probably the engine mounts are bad if idling is good and engine is not misfiring.

Sounds like a misfire is happening. First two things I would want to check is to make sure the fuel pressure is in spec, there is good spark to the cylinders.

HAs the Check engine light been on? Does it come on when you first start the car and go off? Were codes checked in the computer?

Is that 15,000 or 150,000 miles?

A misfire is when one or more of the components are missing to make combustion. That is spark, fuel or compression in the most basic terms.

The computer, (Powertrain Control Module) will store faults. IF the fault is bad enough it will set a code. A scanner is needed ito check them.
https://www.2carpros.com/dia/how_to_scan_trouble_codes.htm

Autozone can check them for free, but they can not diagnose them. IF you have them checked , we may have a little more to work with. You can buy a code reader also.

I'm not sure if there are two problem happening on this or not.

The shaking at idle while in park gives the impression of a misfire. With that stopping when you put it in gear and driving is odd, then the shifting so high begins to sound like transmission related.

The codes may help greatly on this.

Okay, Sounds like the torque converter may be trying to engage is one possiblility. When was the fluid last changed? Unless it was done just recently, I would pick up 10 quarts of Dextron III, drain the transmision and refill it. IT may not take all 10, but you don't want to be stuck with out enough. The capacity calls for 10 quarts.

I would also check the boot on the intake to make sure there are no cracks when the car is put into drive. The movement of the engine may be forcing something away or onto something else causing a performance issue.

Have you had tire balance checked? Any bent rims? Also, a vibration can come from an engine miss. Has the check engine light ever come on? When was the last tune up?

Let me know.

Joe

If it while braking, yes, it could be the rotors.

Otherwise, check the torque on the axle shaft nuts. They should be around 200 lbs.

Check the wheel balance as well.

Roy

Make sure the plug wires are on the correct plugs, check for shorts in plug wires. If check engine light is on, have the computer scanned. Check fuel pressure and compression.

Get the tires balanced and the alignment checked that could cuase the vibration at high speeds like that.

If thats not it the suspension components could be wearing past their serviceable limits.