For car audio stuff, you definitely want to run directly to the battery. Alternator won't hurt, but any "reserve" needed out of the battery is only linked by the "charge" wire between the alt and battery.
First, look up what wire size is recommended for those amps. 10ga sounds WAY small. I'm running 2 gauge to a distribution block in mine, then 6 or 8 gauge to the amps in my truck. I'm running 1/0 to all my boat amps.
Run AT LEAST the recommended wire size. Not sure of the power ratings of the amps, but i often use the largest size the amp will accept.
Then, run both those directly to the battery. Make sure you have a GOOD ground wire from the amps to the body, of at least the same size as the power wires.
From there, add additional grounds from battery to engine block, engine block to body, and battery to body. These should also match the amp wire in size.
This SHOULD fix your problem. If not, you need to look into capacitors, not alternator upgrades.