One other thing... Kodi only supports 'clone mode', which means it only does two monitors with identical resolutions.
Since your laptop "only" has a 1366x768 screen, you will be either seeing Kodi on the laptop screen or the 1080p screen/tv.
You could try forcing a 1280x720 resolution, that should work on both output. The display rate is (almost) similar.
I fixed all problems using this post (although didn't have to create an autostart script because it started detecting the display on a reboot don't know how or why it fixed itself. Quite frankly I don't know how to create an autostart script either so I'm glad ) problem second monitor. I also had another problem where it would get stuck at start screen failing to load xorg and I used the fix from this post [SOLVED] Failed to start Xorg Server help Don't know if this worked, seems like it did, only time will tell.