With the symptoms you describe, something is wrong that I feel quite sure a larger alternator would not fix.

I would start by checking your battery terminals and then move to your audio system connections. Also, have you paralleled any loads on the audio system? You should not have less than a four ohm load. Two four ohm speakers in parallel will apply a 2 Ohm load to the amp, which will theoretically double the current draw.

Good luck,