Yes a new High Output alternator may help but I wouldn't invest in that kind of money just yet. I would do the BIG 3 wire upgrade first.
Here is a nice write up on how to do the "Big 3" wire upgrade.
'How to' upgrade the big 3
Adding a 2nd battery won't do anything unless if you like to listen to your music a lot with the engine turned off. Then you can add a deep cycle battery to your system. But the problem with that is you will be putting more load on your car's alternator which seems like it is being overworked already. Remember the job of the battery is to start the car and to run anything electrical in your car WHILE THE ENGINE IS OFF. When it is on, you are using the alternator. Putting another battery in the trunk is more headaches then what its worth unless if you really need to.
Again, what is the gain set to on both amps?