Good idea using a relay , do you have the circuit or circuits protected with fusible links? The battery is connected to the alternator via a 14 gauge fusible link running to the rad support junction block. From what I understand a 14 gauge fusible link has a rating of 16 amps under the hood [170 degrees] and 30 amps in places other than underhood, don't know if that's correct. You're charging the battery and running your accessories through the same fusible link. You will want the accessories protected just in case.

I also agree with Rohrt, charge your battery fully and give it a load test just to be sure it's an alternator snag not a defective battery.