dual monitors and a single VDU input. Can i have sepearte settings????

I have several PC’s each with just one VDU input on them. Therefore i have used a splitter so that i can have dual monitors. The only issue I am having is that the Monitors keep switching sides randomly. For example i could boot the pc up one day and the monitors are in the correct position. But when i re-boot on another day they decide to switch sides. I can go into the settings and switch the monitors back but this becomes extremely frustrating.

I know that if a PC has two VDU inputs it is possible to set one as the primary and the other as the secondary. But can this be done when using a splitter?