My 2002 dodge grand caravan went crazy.

The headlights, flashers, wipers, radio, gauges all went on and off. It seemed like it was struggling to get fuel, and died. The battery was dead. I got a jump start and it kept shutting off while all the above problems recurring. I replaced the alternator, no fix. We have 4 children and I work so we need it running fast.
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Answers
An alternator can't charge a bad battery, and a good battery can only run the car so long with a bad alternator, or wiring.
If you can at least get the van running, perhaps a friend with a voltmeter can test if the battery is getting any charge at all. But again, if the battery has a dead cell, it might not accept a charge.
Most batteries that are 5-6 years old are running on borrowed time anyway.