automating OSX 10.9.2
See if this AppleScript code does what you want. It should click the menu item "ProPresenter" of the menus "Aux1", "Aux2" and "Aux3" as you requested:

tell application "System Events" to tell menu bar 1 of application process "ATEM Software Control"
    click menu item "ProPresenter" of menu "Aux1" of menu bar item "Aux1"
    click menu item "ProPresenter" of menu "Aux2" of menu bar item "Aux2"
    click menu item "ProPresenter" of menu "Aux3" of menu bar item "Aux3"
end tell


To set this up as a keyboard shortcut, use the following steps:


Open Automator
Create a new Service

Add a single Run AppleScript action to your Service with the following code:

tell application "System Events" to tell menu bar 1 of application process "ATEM Software Control"
    click menu item "ProPresenter" of menu "Aux1" of menu bar item "Aux1"
end tell



Make sure it's set to receive "no input" and work in "ATEM Software Control". Click on "any application", then "other", and navigate to the app.
Save it with a name of your choosing.
Now, go into Keyboard preferences, click on the "Shortcuts" tab, then click on "Services". Your newly created service should be at the bottom. Click on it, and click on "add shortcut" and specify a shortcut to your liking.





Lastly, go into "Security and Privacy" settings, click on the "Privacy" tab, and then "Accessibility". Make sure you see Automator in the list. If not, click on the lock on the bottom left and enter your password, then click on the "+" and add Automator to the list.





Repeat this with modified AppleScript code for each camera you need to switch between, with a different shortcut for each.