If you just grab the standard YouTube embed code (the iframe code is fine) it works nicely on all devices. They way you are doing it now seems just to serve up the Flash version, which i-Devices don't like.
To get the gallery-like effect you want, there are quite a few slideshow scripts out there into which you could paste the standard iframe code.
But perhaps the API discusses this problem and what to do for i-Devices? I'm not sure. I did a bit of Googling, and found discussions on it, but they are a bit over my head.