2001 V6 Very Rough Idle, Won't Go (Sometimes)

[Ol'Jim]

Trying to help out the daughter of a friend, and will only have one shot (this evening) to try and fix it, or at least figure out what is wrong.
It is a 2001, V-6. She said after a short drive, (like to a gas station), she shuts it off, then when she goes to leave, it is hard to start, and "shakes like crazy", and when she puts it in gear and pushes the gas, it does not move. Same whether in Drive or Reverse. If she shuts it off and waits about 30 minutes, it is fine. It has done this 5 times in past few weeks.
She said it does throw a CEL when it is doing this, so I may just drive it to the nearest Autozone, so they can pulled the code(s).
Any ideas, suggestions will be appreciated, only work I ever did on one of these was to replace a soft rubber PCV vacuum elbow that had rotted out. Thanks, -Jim.

(PS: Apologies to Mod - Also posted under Ford Escape, since same vehicle)

[adamgrant]

Sounds like there is some misfiring going on... Their known for ignition coils causing engine shakes and in some rare cases the computer(pcm) have failed on the ground side for the ignition coils. P0301-P0303 are cylinders onthe back of engine and P0304-306 are the front cylinders