You need a high output alt for sure.. adding a second battery only makes your situation worse. now your alternator has to charge both batts and put out 1400w and run your vehicle. Thats a tall order for any factory alt.
you can easy your electrical load by wiring your sub to a higher ohm if its DVC, and ditching the second battery.
1400w from a 13.5v system would require about 103 amps from your alt.. the car needs power too somewhere around 40 amps. you would need at least a 143 amp alt.