If the car stops when it is running then the problem is not the battery. I would check first to see if the batery is being charged. Easily done with a voltmeter (VOM) on the battery, or many parts places will do it for free (Autozone, etc). As you said , you replaced the alternator, so we assume the briushes are new and OK. Most likely is the wiring harness. It shorts together or to ground and there goes your power. That small red white wire is critical as it initiates charging. I think it comes from the dash "charging) light. Check the bulb there and then check the wiring from there to the alternator, it runs under the front of the engine. Many have rewired so it goes along the firewall to right fender to alt.
Best to get a volt ohm meter and wiring diagram for diagnosis.
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