Off the battery? How did you wire the amp? It shouldn't be connected directly to the battery anyways. Once the car is running, the alternator supplies all of the power till demand exceeds supply. Only then the battery takes over. You should be alright with 2nd amp. After all, you have a Sony amp, not like it's giving you 1200w rms.
how should they be connected then? by not directly to the battery do you mean throught a capacitor or fuse?