A properly functioning and installed 200 amp alternator will (not should, but WILL) have plenty of oomph to charge two batteries and two (even two 3-Farad caps) caps. Once a cap is charged, it pulls no more current from the voltage source, unless it is shorted internally. You did not say you were blowing fuses, or that the battery was going dead overnight, so this is most likely NOT the case. Did you address the power cable from the alternator? If you are using the stock charging cable (probably a #12, MAYBE #10) you do not have enough current capacity for that alternator. 200 amps will need at least a 3 gauge, but since finding #3 wire is tough at best, you will have to upgrade it to a #2. You will also need to do the same with the chassis to engine block ground cable, and from the front battery to the chassis. Charging two batteries will not be an issue, as long as they are IDENTICAL! Either two yellow tops, or two red tops, NOT one of each. (I have done it over and over... as long as you have current to keep them both charged, about 2-4 amps each when fully charged, there is no issue.) Do not try to use different batteries, they will be parasitic to one another, and you will end up needing new batteries sooner than necessary. Like Djmajicmark1 said, check the voltage at the front battery and the alternator. If you have the voltage at the alternator, but not the front battery, your charging cable is to blame... replace it. When checking the voltage at the alternator, check it to the CASE of the alternator, not chassis ground. If your voltage is OK there, then check it to the chassis. If this is where the failure is, clean all of the mounting points of the alternator with fine sandpaper, to be certain you have a proper ground. It sounds to me like you have enough power cable in the trunk, sizewise, I do not believe you will need anything bigger, but DO address the underhood wiring.
To test any of these theories, charge the batteries overnight with a 10 amp battery charger, (go ahead and leave 'em in the car, just connect to the front battery) then check your voltage at the amps in the morning... if the voltages are ok, even with the system running, (obviously the average voltage will drop as you play the system, so take that into account) then you know all of your power distribution is OK, and it is your charging system. Check into the alternator and underhood wiring issues stated above. If, when you return to the shop in the morning, and the battery charger is STILL putting out the same or more curent than it was the night before when you connected it, or if your voltage drops RAPIDLY, then one of your batteries is defective, and will need to be replaced.
Give these suggestions a shot, and let us know how it all comes out.
It all reminds me of something that Molière once said to Guy de Maupassant at a café in Vienna: "That's nice. You should write it down."