C402 Captain reported an alternator malfunction during initial climb resulting in a dual alternator failure. The flight crew was able to restore one alternator and returned to departure airport for precautionary landing.

Narrative

Climbing out of ZZZ; on our initial climb vector; the First Officer and I both noticed the right alternator light illuminate. We continued our climb; and I; as the Pilot Monitoring; got the QRH out to address the issue. The circuit breaker had not popped; but the voltmeter showed 0. As per the QRH; I elected to replace the fuse for the alternator; and attempt a reset; based on the facts that it was low IFR everywhere nearby; we were going to be IMC for the entire flight; and there was a possibility for icing - as we had witnessed trace ice earlier that day and there was mixed precipitation supposedly close to ZZZ1; our destination. I followed the steps in the QRH; and when turning the right alternator switch breaker back on; both alternator out lights illuminated as well as the low voltage light; backed up by 0 on the voltmeter for both alternators. Considering the weather conditions; my first action was to [request priority handling] with ZZZ approach; and request a return to ZZZ as we troubleshot. Fortunately for us; ZZZ had just switched runways to XXR and XXL; so we would have a 180 turn from our current track; onto the localizer for XXR. As the First Officer was flying; I opened the QRH and went to the dual alternator failure checklist. I replaced the fuse for the left alternator and turned it back on. It came alive; and I opted not to turn the right alternator back on; as it had caused the issue to begin with. After the alternator came back on and as we were getting vectored for the ILS XXR; I notified the Passengers that we had a minor mechanical issue and that for their safety we would be landing back in ZZZ shortly. They were quiet but not alarmed. Upon landing and shutdown; I explained in minor detail to the passengers that we had a partial electrical power situation and given the weather today; we decided to return back to land and that they would be taken care of. They were cooperative and understanding. I think electing to replace the fuse and attempt a restart of the right alternator caused the left alternator to fail. The right alternator had been having issues and had been replaced a couple days prior.