How Can I Fix My Car Sound System?

I have an Xplod stereo with a 4F dblink cap with two 1000 watts each Kenwood amps and four 12" MTX Terminator subs and a new alternator all in a 2001 Ford Explorer Sport Trac. My problem is that when I turn up the volume at some point the subs stop working properly. They bump at low volumes but if I turn it up they lose their thump and it sounds like they're struggling and if I have my headlights on they start to dim. I also notice that the battery gauge starts to move down when the bass hits and sometimes my stereo turns off or loses power. It doesn't reset any of the settings but the display and other lights on it go off. Does anyone have any idea(s) of what I can do to fix this problem(s)? Help is very appreciated.