Well, tahts always a tricky one.... modify existing modules.... or making entirely new ones? The first requires that you know exactly how the circuit works, so 'tap' it for signals that you need, or remove parts off the PCB, and add wires to extend them (so your headphone jack can go anywhere on your PC case, and isn't attached the the PCB). You can always discard the original jack, and wire up the one on your PC's front panel to it. Just make sure you get the pinouts correct. Front panel jacks in PC's have 5, sometimes 6 wires, but you only need three. L, R and GND.
The second is a lot of work, with the only real advantage that you have complete control over what goes where, and how it works.
I skimmed over the datasheet, and it just looks like a nice stereo power amp. If you look at the recommended supply voltage... its bipolar, that is +V and -V. Now many can work with a single supply, that is 0V (GND) and +V (your 12V) but that mens the output of the amp 'sits' at half the supply voltage (6v). If order to filter out this DC component, you'll see many headphone amps with large capacitors on the outputs .. which I don't see on your PCB.
So I'm guessing the ribbon cable that supplies that module provides +V, GND as well as -V (with the other two being L and R audio channels). From that I think its safe to assume that the audio inputs to the PCB are AC, that is, the signal is centred around 0V (GND). This means that theoretically it
should be fairly straight foward to build your own headphone amp - one that will happily run off a single supply (12V in your case).
As an FYI, as you pionted out the chip requires +/- (yes, that means plus AND minus) 4 to 18V. You are correct in assuming thats DC, few semiconductors are powered by AC
But the current (4.5mA) is what the chip will draw when the voltage is within its supply range, and when its not driving anything on the output. Give it the right power voltage and it'll draw whatever current it requires, as long as your power supply can provide it. If you have a a +/- 12V supply that can kick out a thousand amps....the chip will only take 4.5mA.
If I were you, I would just extend the volume pot and headphone jack with wires
So the PCB can sit anywhere you wish. I assume you're using the whole 'device' (the thing thats attached to this headphone amp), so that will provide lal the votlages already, and you wouldn't have to redesign anything. Of course, now you have a fair idea of whats going on - good detective work on your part - you have the
option of replacing the amp with something you prefer, perhaps a lower noise chip, or one that runs off a lower voltage.
APologies for a massive post, but its always good to keep things clear eh?