Odd behavior in the LMS. I don’t think that should be happening. What you describe is the feature triggering (hence the change in the icon) but it is not going full screen, correct? Until I can test, the only thing I can think of is that your LMS is set to open a course in a new window and maybe that is somehow effecting the full screen feature from working properly? Interesting.
You can accomplish most, if not all, of these things by manipulating the built in mediaelement player, however, the folks at Trivantis/StoneCalibre have made it ridiculously difficult by the way they implement it (don’t get me started..). It is, therefore, MUCH easier to just pop in your own version of the player when needed to give yourself simple and complete control over all it’s features.