I have a 2000 dodge Durango our battery died a few days ago thanks to the kids leaving my lights on ! Needless to say we jumped the battery and it ran fine for two days ! However now it dies if I let my foot off the gas " idle " I can set it in neutral and switch it into drive and it runs just fine until I have to come to a stop and instantly once my foot comes off the gas the car dies ! Any ideas ???

SOURCE: 2000 Contour dies at low idle

you could try to clean the mass air flow sensor

SOURCE: 2000 Dodge Durango Won't Start

You might want to Check electronic sensors, like would you start with the idle control sensors.Also Try tot urn the ignition key to the point just before the engine starts to turn over And leave the key in the that position. If the fuel pump is located inside the gas tank,remove the gas cap & listen for a "whirring" sound. This sound means your electronic pumping is working.

SOURCE: when engine is warmed up the car begins hesitating

I really think it's the TPS, (throttle positioning sensor) on the throttle body. When this sensor is defective or out of position the vehicle will idle like that and even stall. If you haven't had it scanned, you should do so, that will probably tell you the problem.

SOURCE: rough idle, dies when trying to give it gas

it'll either be your ignition system (spark plugs, distributor cap, etc) or more likely your fuel system (most likely your fuel pump or your fuel filter)