Check engine light on? Codes? If not you could have some water in the tank. When it sits the fuel an pool at the pump sump screen. When you start it the water goes directly to the injectors. I would add some good fuel additive that will remove water. Cheapest thing you can try. Years ago in a Mopar training class the instructor said you can replace every part on the car trying to fix it. He said you cant fix bad gas or poor contaminated fuel.

2003 Dodge Durango, 4.7, 30,000 miles.

strange issues that keeps recurring, after you drive the vehicle and it gets warmed up.

When you shut off the engine and it sits for a little while, 3 minutes to up to 30 minutes, vehicle starts up fine, after about 10 seconds running, in drive or in park, there is no throttle response, engine has no power and motor is stumbling. I can put it in neutral and after a few seconds it runs fine, after that you can drive it with no issues, fuel mileage is good, changed spark plus and air cleaner. I cleaned the MAP sensor. There are no codes. I checked for vacuum leaks no observed. no smoke from tail pipes.

It does not happen on initial start up or when the vehicle cools down sufficiently.

Any thoughts would be greatly appreciated.

How old is the battery? I've seen some weird stuff happen when the battery starts going bad. I'd get it tested, after it's warmed up or just verify that the cranking voltage isn't dropping below 10.5V when it's acting up. If it's good, then move on.

I have heard of cleaning a MAF sensor but never a MAP sensor.

My 05 minivan does the same thing after a fuel fill-up. Especially if ambient temps are up there.

Was told there is / was a recall to replace the fuel tank , causes a vapor lock type issue

it stumbles and almost will not pull itself , till maybe 10-15 seconds after its running.
Only does it if the tank is near empty when I fill it up. . And the hotter outside temsp are, the worst it is

have you tried running it with the gas cap loose or off ?
just tossing that out there. it won't cost anything to try.

I wonder if you guys may have a leaking purge valve allowing fuel vapors from the tank into the intake manifold. This is like flooding an engine. Or a even a fuel filled cannister. That can happen if you continually top off the tank after the pump automatically shuts off.

I will check and see if the canister has fluid in it. I will have to check if and where a purge valve would be located on my vehicle. Thanks for the thoughts though.

Edit, yes it has one....https://www.partsgeek.com/jf6kf2w-dodge-durango-purge-valve.html?gb=pp&cid=28884375&aid=4168799306&kid=1100003048023&msclkid=f1b81eafa5081f2d5699400704dfd4ad&utm_source=bing&utm_medium=cpc&utm_campaign=Shopping%28BSC%29&utm_term=1100003048023&utm_content=Dodge&

I I know it has one. That valve should be closed when the engine is off. If it leaks or is hung open (possibly from charcoal particles when a canister comes apart from gasoline contamination) could cause the problem especially when hot.