Two Different Systems Running Simultaneously.

[Emilio Guifarro]

Here I am again with a topic more complicated (for me)
I have two systems running the same show.
FIRST ONE: I have an hp laptop windows 7 pro, I7 @ 2.+ ghz, graphics NVidia quadro @ 2ghz and 2 gb dedicated.
Second display ports available: DVI-d, HDMI and DP.
I run karaoke in mp4 format, karaoke player is from karaokanta,
SECOND ONE: Desktop, windows 10 pro 64 bits, 500 gb HD, 4 gb ram, Quad core @ 3.2 ghz, graphics Radeon 6800 HD with 1 gb dedicated, second display ports available: DP and VGA. I run in this one Hoster 5.1.
The reason I use two systems is because in the first one I play only a package of music very well protected for karaokanta and can be played back only with their on player, even though is in format recognized by Hoster.
My problem is to hook up the two pc's to a projector, and with a switch just select which computer second display, I want to show to the audience. I tried a KBM switch and did not work, also I tried an HDMI switch and worked but, with
this issue: Everytime I selected the display I wanted to show to the audience, the second display configuration on the pc not being shown to the audience would reset.
And, running both players in the same computers cause one of the programs crash.
Does anybody knows of a hardaware to solve this problem (if any)? Or any other option?

Thank you