I'm not sure I can give a satisfying answer to your question, but perhaps I can enlighten a few things and point at some potential solutions. I take it you have two individual TV sources, or one TV source with two listings? Kodi see's all TV sources in the library as one flat file and doesn't distinguish between sources. In file mode you can access separate sources independently, and for most skins; file mode (it should really be called file maintenance mode) will not look much different than library mode with some exceptions, sorts, artwork, how seasons are displayed and specials handled (and some of the library extras that each skin imparts).
So clearly library mode is the preferred view. To accomplish what you want, there is a number of work-rounds, the first is to use a rule with smart playlists (should be easy to set-up with a 'path' rule), once you have your library set-up with two smart playlists (one for TV-offline and one for TV-current) mark them as favourites and link them to custom home page buttons (skin dependant, then hide the TV button}, and call the new custom buttons as you wish. Another choice would be to establish new nodes for each
Video nodes (wiki) there's also a node editor that makes all of this pretty easy (very similiar to smart playlists) and again make custom buttons for these new nodes. Last but not least is an add-on worth exporing for some
Add-on:Super Favourites (wiki)
Missing artwork in file mode, usually can be elevated by running artwork downloader, tick the boxes seasons etc. and you should be on the road to populating those blue default folders. In some rare circumstances you might have to manually choose season posters and a few things that library mode would support.