My child theme inlcudes php as well as css files. Whenever I switch to a different theme for mobile browsers it works but the custom post types, cats etc are missing in action. I am kind of lost.
Your problem is that you’re doing too much with the theme. Themes are all about presentation, not about functionality. If your child or parent theme is defining a custom post type (as I infer from your question), then you’re doing it wrong.
When the mobile plugins serve up a different theme for your site, they ignore the main theme for your site entirely. That means no CPT support on the mobile side unless you rewrite the mobile plugin yourself.
So, instead, spin off your CPT definitions into a plugin so that they’re still available to the mobile version of your site.