Not shure if you are talking a real APP (dont know anything about that)
but if its a WEBAPP (a normal webpage that tries to look as a real APP),
Then the only way i found to prevent youtube-videos from opening in Safari/Qt-player
is to embed it using "Fancybox" (maybe other boxes also).
that will keep it on the page in Youtube´s own player.
You can even have a original playlistplayer.
I stopped trying to embed youtube videos on iPhone-pages (to small)
I tried to include a link to a jSfiddle-example but this forum wont accept it
it forces me to write the whole example here...which i´m not going to do
because that is to much work for me right now.
(dont know how others are allowed to link to jSfiddle)
This forum is way to dictative to my taste.
Anyway you should be able to (incase of a webapp) find info at Fancybox´s website.