In my continuing quest for peace and quiet, I talked it over with daisy_knotwise and we picked up another computer for the bedroom so that either Gretchen can use one computer while the girls battle over the other or she can retreat from the field and let them each have a computer to play on. The new, small computer desk arrived today at the same time as all of the computer parts and I got everything assembled and set up this evening.
So far, everyone's happy. I'm going to try to keep it that way. :)