[ImperialCrown]

I have seen the rubber weatherstrip at the rear of the hood and cowl drain hose plugged or missing cause this. Water will pour in on top of the motor and get down inside the spark plug tubes. You may find rust and white powdery corrosion left behind from the water when you pull some plugs toward the back of the engine.
There is a couple of PCM flash updates for setting false O2 and EGR, etc. fault codes. If you are under 80K, this may be covered by your federal emissions warranty. The latest and greatest PCM software would be desirable. Has the cluster recall (G07) been done?

 

[B10alia]

I have no experience with these trucks but it sounds like an ignition problem to me. Water on broken insulation could be shorting your ignition system out, which will cause a misfire (chugging as the engine misses on one cylinder) and a temporary check engine as the computer picks up the misfire. Where the water is coming from and which component is shorting, I have no idea, quite possibly ImperialCrown's suggestion.

 

[RIck53209]

We just had one of these in our shop with the same exact problem. Found the intake manifold gaskets leaking. If you start the truck, drip some water (out of a water bottle or something small. you wont need a lot) right next to the intake gaskets on the passenger side, if you can do it without getting the coils wet then you know it is the intake gaskets. The only way the dealer sells the intake gaskets, is with the updated intake manifold. (Apparently this is a very common problem). We also found on this (and many other durangos) that part of the wiper cowl on the passenger side is not there. When this part is missing, it lets rain water come down the windshield and drip right onto the coils/intake manifold. Chrysler really screwed up here. We could not even find these parts in any diagrams until you look at diagrams for an 09. The part numbers of these missing pieces are 55362513AE (a/c air duct) and 55056417AD (baffle).

Good luck,
Rick