Car shakes when downshifting and stalls sometimes

That sounds like a torque converter that is sticking in lockup mode. That means that when it shifts, or you are coming to a stop the converter doesn't slip like it should because it's locked. Changing the fluid might help but, in all likelihood, it is going to need to be rebuilt. I say rebuilt because with that mileage and needing to be removed to replace the converter it would be a good idea to do it all at once. It's possible the issue is a failing solenoid but usually those fail by not engaging the lock-up, they don't cause it to stick.
https://www.2carpros.com/articles/how-to-check-and-add-transmission-fluid

There are a lot of them in the salvage yards so you might be able to find one reasonable and swap it out, depends on your location, the you-pull-it yards around me get about $200.00 for a used unit but you have to be choosy getting one, I usually look for a car that was damaged, like a rollover or rear ended or the like, something that says it was actually being driven before it came to the yard. The ones that look like you could drive them home scare me, why would they be in a salvage yard unless there was an engine or transmission problem taking them off the road. Now if it's a bad engine the transmission could be okay, but that's a judgement call.

As for the service it is a routine drop the pan and filter type, just be sure to use Mopar ATF +4 type fluid, the 62TE is a bit picky about that.
After you have the filter and pan back on (silicone for the pan sealer) add in 4 quarts and start it, run it through the gears and then check the fluid level, you want it roughly 3mm below the low mark to start. Now run it a bit and then check the level hot and add as needed.
Let us know how it turns out.

I wouldn't bother with the fix fluid; it usually isn't a good thing in those units. The symptoms say a sticking lock up in the converter. It is basically a clutch that is supposed to engage and eliminate any slippage between the engine and the transmission. If it doesn't release properly it acts like a clutch in a manual transmission and causes shudder and stalling.
There should be a tube on the side of the transmission where a stick would go. If you google "Carava /Town and Country 62TE Transmission Dipstick Hack" you should get a South Main auto video showing a nice easy method to check the fluid using the dipstick you have in the engine, just wipe the engine oil off first.

Overfull can cause issues but usually not that one, although it's possible the fluid cannot cool down as well. Just be sure the dipstick isn't going in past the stop in there or you can get the wrong readings. I don't recall if that van has the transmission fluid temperature on the driver's info center. On some you can go into the menu and pull up oil pressure, water temperature, transmission fluid temperatures. Makes it easier to check the level.