Switch to alternate 2 computers and dual monitors
What you probably want is a KVM (Keyboard, Video, Mouse) switch that supports dual monitors. It's a simple device that allows you to plug multiple computers into one set of monitors, keyboard, and mouse and switch between controlling them.
I don't know of any that support mixing analog and digital connections for the monitors, but using a VGA to DVI adapter for one of the monitors should solve that problem cheaply.
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