Is there a hot key to refresh a browser that is in the background?
You can put either of these in an Automator service using a applescript Action.

Then set a keyboard shortcut with the Services in keyboard system preferences's Keyboard Shortcuts. 

Note the  'Service receives' settings in the screen shots. This will make sure the Menu appears in all app's services.
(The other apps may need to quit and re open before they pick up the short cut) 



Chrome.

tell application "Google Chrome"
    reload active tab of (get window 1)
end tell








Safari.

tell application "Safari"
    tell document 1 to do JavaScript "javascript:location.reload(true)"
end tell








Services.





Service Menu -In iTunes