amp for four 12 alpine type r 4 ohm dvc?

If you're having all kinds of electrical problems from your current amps, sure its the amps fault, but its also the cars fault for not being able to keep up with the added load. As posted before, you NEED to get a higher output alternator. The one that came on the car maybe an HO unit, but its there for a reason and you said it yourself...everything in the car is electrical. Now you're trying to add in another 200A worth of current draw and its obviously taking its toll.

Bottom line...

1) Get rid of the capacitor, 4AWG wiring, stock alternator

2) Replace with new HO alt, AT LEAST 0AWG, and possibly even another battery.

p.s. make sure you address the Big 3 as well as all the grounds for your amps.

A capacitor only adds to your failing alternator problem. As has been said time and time again on this forum, the alternator is the absolute root of all electrical in a car. It supplies the power, a battery and a cap only store it. Caps are basically band-aids for a cut on a major artery. As far as the new HO alternator, since they dont make one for your car, you might have to fabricate a bracket to make one that is close to the same size fit. With enough time and ingenuity, anything can be done.  

Also, your ground wire NEEDS to be the same size as your main power cable. Not a lot of people realize that (correct me if I'm wrong DYohn) the same amount of current runs through the ground as does the positive cable. That is most likely one of the reasons for your problem.