My logic is pretty much similar to Brooke's. That said, if you have more than one screen, you can make AH run in one screen which allows something else been run on the other screen(s). But if you try to start another instance nothing happens. At least nothing happened when I tried to get two login screens. Not even a message that AH is already running. Thus virtual machines are the only way to run several AH games on a single computer.
But: With virtual machines you'd be sharing your resources even more than you would having two games running. You'd be running double or triple Windowses with all their background clutter as well. Not to mention that bouncing between VM screens is even clumsier than Alt-Tabbing. Most likely you'd be getting complaints about bouncing all over the screen...
Keeping your controllers up to the task in each window might also be problematic, most likely you'd crash your planes because of the controllers staying on one screen when you're jumping to the other.
So several computers is the only viable way to go. A relatively inexpensive option might be getting a mediocre used gaming laptop for the "slave" set of bombers. I have no clue, though, how much anomalies the secondary set would cause on your primary screen if the resources are too limited. Then again, on that secondary PC you can strip all the eye candy to the bare minimum to speed up the gameplay.
