I have a similar problem with my external superdrive in 10.11.2:
CD/DVDs cannot be inserted when the drive is plugged in while system is running. Rebooting with the Superdrive connected solves this, but the eject key on the keyboard does not eject the media in the drive. CD/DVDs are ejected when they are dragged to the trash or after right click -> eject. Other funcions of the eject key on the keyboards are working (e.g. ctrl + eject).
So I exclued hardware failuers related to any of the devices and after starting from my bootable backup of 10.10.5 with an exxternal drive the problems disappear. So for me it's an OS related problem of El Capitan.
Talking to the apple support they advised a reinstall that changed nothing at all.
Another post suggested to use the command "drutil eject" in the terminal and do an SMC reset afterwards but I was not able to test this. Maybe this solves the problem for you.
Otherwise I am hoping for 10.11.3 to fix it.