You can accomplish what you want in a couple of ways, but in my opinion the best way is to instead buy an external DVD writer that can be connected by USB, and then move it around when you need to use it on another PC.
If you insist on installing the DVD writer internally, things become more difficult:
You can share a DVD drive just like a harddrive from within Explorer which will work for most program installs (but probably not when installing copy-protected games).
The old Nero 6 has a NeroNET add-on that makes it possible to burn to a CD/DVD writer on another computer, but if you don’t have Nero 6 already, this is not going to be a solution, because NeroNET isn’t supported in later versions of Nero.
You could also use your burning programs to create an ISO image, and then either copy it over the network to the computer with the DVD writer and then burn it to disc from there, or create an ISO image on a network share, and then mount the network share on the computer with the DVD writer and burn to disc from there.
Perhaps there are other ways of burning over the network using the iSCSI protocol (never tried it myself) or by using other advanced burning software, but I’m not sure.
I reiterate that I think an external DVD burner that can be moved around is better than trying to use the network for burning/reading DVDs.