OK, thanks for the explanation! You will need to remove the styles that make your menu tree collapsible on small screen devices. I am not sure which theme you’ve used (since it’s obviously modified for your needs) but basically you will need to remove all media queries from the theme – i.e. just delete everything in the theme CSS file after the following comment:
/*
---------------------------------------------------------------
Responsiveness
These will make the sub menus collapsible when the screen width is too small.
---------------------------------------------------------------*/
Cheers!