Neither setting causes the display to switch from the lcd monitor (#2 in Control Panel) to the large screen (#1 in control panel). We are not running 'Extended Desktop' with our video card - could that be the problem?
Yes, that's the problem.
If you are using them in "Mirrored" mode (extended desktop off, same content on both screens) then Windows "sees" them as only one monitor.
If you are using one of the GPU-vendor-provided super-fancy-extended-desktop-modes (like AMD Eyefinity) then the entire monitor "surface" shows up as one big monitor to windows. The displays control panel still sees the actual individual monitors in case #1. In case #2 the Windows control panel won't even see both monitors.
And, lastly, if you are only using one active monitor at a time (and disabling the other one) then you can't use it from an application because, again, Windows only "sees" one active monitor.
In any of these cases, you can't use any kind of automated monitor switching system in any application.
You'd almost certainly be better off leaving that small screen enabled all the time, putting Windows in extended desktop mode, and then using the monitor switching built into MC and maybe an add-on utility like UltraMon (which is great for multimonitor setups) for other applications.