are you playing your system with your car off? Don't know how many watts your running, but I would say, just upgrade the battery under the hood. I'm sure your running less than 1500rms correct?
Just adding a battery in the trunk without hooking it to starting battery or the alternator, will just drain the battery until its drains so much there is nothing left to power the amps. If you did hook it up, with stock alternator, it would actually draw more current from original battery AND over draw the alternator to death because it constantly has to charge two bats.You will need a high output alternator for 2000watts RMS.