You really have to watch current draw. Chances are your car's alternator is rated somewhere from 80A to 120A depending on the size of your car and it's power requirements. The manufacturer isn't going to put an alternator in that has tons of extra capacity sitting around. Basically, if you have Air Conditioning, Power Windows, and other bells and whistles like that you can rest assured that you have a little extra current sitting there.
But surely you've used it all up -- TWO amps, plus a carpc will draw quite a bit of current (M1-ATX can draw 7A alone). If your battery isn't charged it's a tell-tale sign that you've overdrawn your alternator's current max and fried it -- so your car and all of it's electronics had to run off the battery... draining it.
And yes, there is a huge difference between batteries. When you say Yellow top and Red top I assume you are refering to Optima batteries. The Red top is designed for pure starter power, a better battery than normal however not ideal for electronics. The Yellow Top batteries are designed to withstand discharging better than a normal battery, and also take something like 40% less power to charge vs. a "stock" battery... placing less current demand on your alternator. From what I gather a typical battery can take up to 10% of it's Amp-Hour rating to charge. For instance, I added a 7.2Ah sealed lead acid battery to my car for my carPC -- so I know that it's taking an extra .7A of current to charge.
Anyway. Hope this makes sense. If you're running two amps I'd strongly reccommend getting a 1 Farad capacitor and also if you are looking to get a replacement alternator call your local car repair place to see if anyone will rewind your old one. Usually they can rewind an old alternator MUCH cheaper, and even add extra capacity while at it. Just don't add too much because the housing of your stock alternator wasn't designed to take 200A and it will melt!
I hope this makes sense and helps!
Mark