Have you tried other themes to see what behaviours and properties they have? Many themes are different in the way they show the presentation layer.
With your current theme, what you see on mobile is the expected theme behaviour and any changes on the mobile view only would require a lot of coding. Have you spoken to any experts about getting somebody to program the mobile theme code for you? If not there is one I highly recommend and who does good work for cheap → www.taskhusky.com.
Drop them a line and see what they suggest as the best mode of action?