01 Nissan Maxima....alternator problem?

Alright…my 01 maxima is causing myself and my mechanics headaches. This has happened three times: after driving for several hours, the battery and emergency brake lights come on. After about 5 minutes they go off and the airbag and abs lights come. They go off and after about 5 minutes the car goes crazy…gages bouncing around, car losing all power then regaining it and then it dies. The first two times this happened we were able to jump start the car and it acted fine for a month or two. This last weekend was a different story. We could jump start it but as soon as we took the cables off of the battery the lights would dim and the car would die. I finally got it to an auto zone and had the alternator and battery tested. Alternator was fine, battery was not. I replaced the battery and the car would not start at all. I replaced the positive cable clamp and cleaned up the negative clamp. The car started, then died, then started and didn’t die. I took it to a nissan dealership and they said the alternator tested bad. As I was about six hours from home I towed it home and took it to a different dealership. They can’t find anything wrong with the car, the warning lights are off, the alternator is testing fine, it acts as if nothing is wrong. In two weeks my wife and two little girls are needing to take it about 300 miles. We don’t trust it. If we could diagnose and fix this problem we would then start trusting the car again. Any suggestions and advice would be much appreciated.

Check the accesory drive belt and see what it does, it problem continues go for the alternator. The belt might be slipping to cause this.