My current 'active' theme on WordPress is not mobile-friendly so I recently added a mobile-friendly theme (currently 'inactive'). I intend to keep my old theme active for desktop and use a theme-switching plugin so it displays the 2nd theme to mobile visitors only. However since this theme is 'inactive', I cannot edit it in the "Appearance -> Customise" screen. I tried using Theme Switcha & Theme Test Drive to edit it but they didn't allow me to save the changes. Is there any way at all to customise inactive themes and save the changes without having to activate/publish the theme?
While it is possible to have two themes being "active" together, it is not a setup anyone is going to support, and you are going to be "step into walls" time after time.
As an easy example, you will have harder time configuring caching, if it will be possible at all.
Do the right thing and make your current theme responsive, or switch to a better one.