01 Neon poor acceleration

Has the Check Engine light turned on while you're driving? If so, there are diagnostic fault codes stored in the Engine Computer. Most auto parts stores will read those codes for you for free.

"when I put it in neutral it stops"

What stops, the engine or the shaking? You may have a simple misfire but that should be detected by the computer. A worn or broken engine mount can cause a horrendous vibration that will change depending on how much load is on the engine and whether it's in gear or in neutral.

The first thing to do is see if there really is a misfire occurring that isn't being detected. One thing the mechanic can do is connect a scanner that reads live sensor data and view the "AIS Steps". That's the automatic idle speed motor. Out of 256 positions the computer can set it to, step 32 is typical for maintaining a normal idle speed on a good running engine. If one cylinder is misfiring, that will jump up to around step 50 or higher.

Ahh, more variables. The throttle position sensor just tells the computer what you're doing. It has very little effect on how the engine runs. Did you replace the parts to try to solve the problem or did the problem start after those parts were replaced?

Wrong conclusion on the misfires. Three things are needed for a cylinder to produce power; fuel, air, and compression. The one that causes the least problems by far is compression. Just because it was good means nothing as far as misfires are concerned.

Chrysler has the least trouble with injectors among all manufacturers so look at them last. Most misfires are caused by ignition problems, (spark plugs and coils). That would be typical of the shaking you mentioned.

Low power can also result from a plugged catalytic converter in the exhaust system, although that will make the engine run uncommonly smoothly at low speeds. You'll also hear more of a hiss from the tail pipe instead of the normal "putt-putt".

Low fuel pressure can cause running problems, but the typical things that happen usually result in stalling while coasting, not while accelerating. I'd suggest borrowing a pressure gauge but the readings don't mean much because they change according to engine load. If there's no fault codes, the best plan of attack is to connect a scanner to see what the sensors are reading. Otherwise you're guessing and that's the least effective and most expensive way to diagnose it.

Very uncommon on Chryslers.