Hi Michael,
Can you check this mobile menu resolution.
The demo doesn’t have sub menu as Omega parent theme was created as starter theme. Most Omega child themes support sub menu on mobile device.
WOW! you have a crazy amount of nested menu items!
since there is no ‘hover’ effect on mobile devices due to a lack of a mouse, it makes sense that you don’t see those drop down items.
From a ui/ux perspective I would consider the need of your mobile user and adjust the menu accordingly. there may be a way you good implement a slide over menu that shows ALL options in your menu without the need to interact with a parent element.
In my honest opinion I feel your issue isn’t with the menu itself but rather the structure of your menu. Try to revisit the architecture a little bit. Not all problems are solvable with code alone…