I think you need to rework your navigation. You might have too many styles affecting it. Also, I see a top level list item being closed after the unordered list has been closed.
My suggestion is to use one style or framework first. If you are using Bootstrap; strip all the non-essential styles out of it and use ONLY Bootstrap supplied classes and ID’s. Do not add you own classes or ID’s until after you have it working how the framework states.
If you are still having issues, create a list of how you want it to look and that will help us understand what it is you are trying to accomplish.
The main things are– do not combine framework styles for the same entity, and write the code how the framework is designed to work.
I’d rather see you write the code correctly rather than trying to find a hack. There’s no reason why your navigation shouldn’t work if you’re using Bootstrap–and that’s for ALL browsers. I use it and had no issues with any of my devices or browsers.
You’re conflicting somewhere and instead of guessing, just start all over and start small.