Please add the playsinline=1 parameter to the embed video URL. Add the ? or & before as appropriate; ? if the only parameter, & to concatenate with other params (if they exist).
Example:
<iframe src="https://www.youtube.com/v/VIDEO_ID?playsinline=1"> </iframe>
Also, please make sure that the plugin supports an inline attribute. You can also add this attribute manually: https://stackoverflow.com/questions/5054560/can-i-avoid-the-native-fullscreen-video-player-with-html5-on-iphone-or-android