My caprice stalls out in drive.

This sound like it might be a transmission issue. If the revs are dropping as you are at idle something is 'Dragging' the revs down and the delay is the engine and transmission trying to catch up with each other. A test you could try is the next time the revs start to die drop it into Park and 'Blip' the gas pedal to get the revs up then put it into Drive to pull away.
You may need to take it to a Transmission Specialist to get them to look at it.

First off, how new is your battery and how many miles on the D? Dodge vehicles are very sensitive to a failing battery. Have it load tested, and if is the least bit flaky, replace it.

After that, the TPS or throttle postion sensor is your next.

As far as the revving up and down above 3000 rpm goes, that is the PCM protecting the engine from over revving.

To answer your question I must put this in two parts , Firstly if the idle is low and you shift from park to drive and the engine stalls this is due to the idle being too low. When you shift from park to drive the transmission puts extra load on the engine causing it to idle lower and thus can stall. Remedy to fix is to either screw up idle adjuster but most times it's because of built up carbon in the intake throttle body causing the accelerator flap inside to not fully close . This causes the throttle positioning switch mounted on the side of the throttle body to send the wrong signal back to the computer saying that the car is not at idling position when it is. Remedy to fix this is to spray in some Carby Clean into the throttle body and then some more while the car is running, all while holding revs up on motor so it will not stall ( use the whole can ).
Now the second part is that you can have a bad wiring problem with either a broken wire or bad connector . When you put the car into Drive from the park position the engine will rock ( this is on all front wheel drive vehicles ) If you have a broken wire or bad connector some where between the motor and cars wiring loom by the engine moving it can open circuit any connection that controls engine running . Remedy to fix is to put the car into park and physically move and jiggle wiring in engine bay until symptoms occurs , then it's up to you to repair the fault

Try changing the fuel filter. It may have been clogged. If this was at all helpful, please rate. Thanks for asking.

try the EGR valve. replace it or clean it the EGR ports may be clogged as well

your fuel pressure regulator is bad, replace it!!!

check your TPS throtel position sensor. and the vehicle has a rev limiter so it wont over rev n park and nutral. but thats the first thing i would check do to many TPS's wear out and can get dead spots in them.

How many miles on your caprice.

keep an eye on it it may have had a blockage somewhere that has now cleared if it happens again i will try to help out with info