How to share YouTube video on Facebook and make it work on iPad?

I am creating a website that allows the user to watch videos. The videos are posted on YouTube and embedded on our website. We would like the user to be able to share our site on Facebook and install a video on the Facebook wall.

We are working using Open Graph tags, but there is one problem: when using Facebook through an iOS app or through iOS Safari, an error message appears: playback is not supported because it requires Adobe Flash. Please note that sharing the YouTube.com url will auto-disconnect to HTML5 and the video will play on the wall.

How can I make my video play on the wall? Or at least how can I make a video link link to our site instead of triggering an error message?

See our site example here: http://m.gad.dk/at-overleve-med-en-alkoholiker/film/

Thank.