RE: Durango cuts off at a stop
Do the key on, off, on, off, on exercise and see what code pops up in your odometer display.
From what you describe, could be a bad or dirty IAC (idle air control valve), throttle position sensor (TPS), or just a dirty throttle body.
Get back to us with the code, and we can go from there. Also, if your battery is older than 4 years, or is questionable have it tested.
Our Durangos are well known for terrible idle/driveability issues when the battery is on its way out.