And I was also going to say, what's wrong with the lights dimming when the bass hits anyway? That's like complaining because the rear view mirror blurs.
To get a better idea of what is going on, put an old-school analog voltmeter with a big meter scale across the battery terminals and see how much the voltage dips, and do the same at the amp power terminals. If you see a bigger dip at the amp than at the battery, the power wiring is weak someplace. Next hold the plus lead at the battery + terminal and the minus at the amp + power terminal, and measure the voltage drop through the plus path directly. To check the minus path, hold the + meter probe on the amp - terminal and the - probe on the battery - terminal. Then measure across each connection and find which is the weak link in the chain (highest voltage drop).