The reason for the two networks is that my modem-router is electrically incompatible with one of my computers.
hmm, I never heard about such things)
Is your electrical grounding configured correctly?
In my country some old apartments do not have third (ground) wire. I've seen a lot of glitches because of that.
Have you tried to install an ethernet switch?
You can connect your modem-router to the ethernet switch, and connect all PCs to this switch. It may help.