In order to split all those up, You need a sound card for each. Onboard can do 2(if you split the front and rear outputs.).
So unless you want to install all kinds of cards, that may be interesting. On the other hand, 1 computer with lets say Skype, music ect may work while the other will handle games and such. In that case, you could just use the computers volume.
Anyway, Something you may wish to look at(more so the "simple virtual earth mixer with input attenuation(level control)").
http/www.all-electric.com/schematic/simp_mix.htm
Important things to know.
1. That shows 1 channel, you will want variable resistors or pots that can handle both channels at once.
2. Opamps are more easy to work with if you have a symmetrical power supply(-9v 0v +9v). This is the hardest part.
This is for a pocket headphone amp powered by 2 9 volt batteries. It WILL let you get symmetric voltage from a normal single voltage power supply. If you like to play, you may also look at dc-dc converters that can turn one voltage into a negative 0 positive voltage as well as isolate the system.
http/tangentsoft.net/audio/cmoy-tutorial/misc/cmoy-tangent-sch.pdf
You NEED an isolated power supply(wall wart that has its positive and negative NOT connected to any of the power prongs.) for this to work.
Now, if you combine the 2 setups, you can make a mixer with volume per input AND place a headphone amp(also note that you can find many more modified designs for the amp by Googleing
cmoy amp) at the end(if you setup to be able to connect the amp to the mixer with a cable, you can also use a amp or receiver to replace the headphones in the future.).
This is NOT a small undertaking. I have made a 2 x 5.1 in 1 x 5.1 out without volume control and just a basic upmix feature(
Image<- and NO, the heat sinks are NOT needed, I am a computer guy and heat sink anything i can) and it works well for me. You project is much more. If you are a tinkerer, get your self a
bread board and have fun
I am not that advanced in this type of thing, mine was a project of necessity, but I will try to help if you decide to build this.