Using remote desktop to control a computer also connected to a projector

Question

I'm planning to have a small PC that lives in a box, which we can connect to a projector and then access wirelessly via RDP. That way, the computer lives onstage, while I can control the presentation it's displaying from afar. To do this, I need to have the computer display the "control" screen over RDP, while still having the projector physically connected to the VGA port.

How can I configure RDP to use a "virtual" monitor for RDP while still allowing the programs we run from RDP to show on the real monitor?

If it helps, we already have an external USB display adapter that we can use for the projector connection, if there's something special about the computer's VGA port that allows RDP to do its thing.

(I'm not tied specifically to RDP for this. If RDP can't do this but another screen-sharing solution can, I'd be happy to use it [as long as it's not too expensive].)