I've had this issue since I purchased a few months ago. It kicks and jerks while driving. It runs and idles fine, but it doesn't always run smoothly. It'll happen even when I'm not shifting, so anything related to the tranny has been ruled out.

Auto Zone ran diagnostic and pulled three cylinder misfire codes.

Took it into the shop and they pulled a code to replace the crank shaft sensor. When the work was done, it wouldn't even start up. Tried another sensor from another brand and had the same issue. Put the stock one back in, and it starts, but we're back to square one on this mystery issue.

Plugs, wires, cap and rotor, ignition coil have all been changed out recently.

Any help would be greatly appreciated. Thanks in advance.

 

could be bad O2 sensors...
or the wiring to the O2 sensors...there is a known issue of the wiring under the exhaust manifold melting...
hope this helps

 

I'd figure out why the new CPS sensors aren't working. check the wiring for those too. It sound exactly like CPS symptoms.

i had rear 3 cylinders misfiring also. look into upstream o2 sensors, check for vacuum leaks. if that doesnt pan out, maybe intake/exhaust manifold gaskets.

 

Is it an automatic or manual?

 

Aftermarket CPS suck and I've gotten many bad off the shelf from big name part stores. As long as your old one works that may not be the problem. However it never hurts to have a OEM mopar part on hand for when you may need it.
As per your issue, look closer at the codes but these are my first guesses:
Get a fuel pressure gauge and check fuel pressure to make sure it's OK.
Then I'd suggest to run the engine for a few minutes, don't let it get too hot or you'll burn yourself...turn it off and pull/check each plug. Check for fowling and for excess fuel. This will narrow down the cylinder/s in question and may be a leaking/faulty injector.
Excess fuel = fouling = O2 sensor to lean fuel = starved engine under load.