1999 Cougar electrical problem

Have a problem with 1999 Cougar 2.5 V/6. When you turn the head lights on the engine will quit running, if you turn the headlights off the the engine will start running. When it is doing this if you leave the headlights on and turn the key to start the engine the starter will not work, turn the lights off and he car starts right up. This does not happen all the time. Have driven car for as long as two weeks and no problem. Sometimes reving the engine will help. (3,000 or 4,000 RPM for a few seconds). Took to Ford said alternator was bad and replaced alternator. Did not fix drove for a while and same problem. Sometimes the dash lights will flicker a little. Also sometimes if the switch on the interior is set to come on if the door is open this will kill the engine, flipping the switch off allows the engine to run. Car now has 41,000 miles on it.