Hi,
I see you would like users of your Facebook app to be able to watch a YouTube video(which pops up) right within the app having your logo as a clickable button.
Does the app exist already or are we building a new one?
But which ever way, i'd like you to know that facebook apps run in iframes on facebook which load them from remote webservers via secured connections.
This has two implications,
1. you must have a webhost that grants you access to connect via SSL. This isnt difficult to get.
2. The video cannot popup outside its designated iframe on facebook except when in being viewed in fullscreen.
I'v got over 8yrs experience developing applications and i'd like to assure you that I can get this done for you in very little time.Cheers.