You can simply set position of nav on resize. Also, you don't need to recreate draggable on each resize, you could update snap value like in example below or use function to calculate snap position. (Check docs to see how to use function to calculate snap value.)
See the Pen eYXGPOa by Sahil89 (@Sahil89) on CodePen
I never used MooTools selectors, problem is with GSAP selectors while using it with MooTools. To prove my point check my last code where I use jQuery selector and code works fine, removed $() to get rid of jQuery selectors and GSAP fails(in presence of MooTools). Remove jQuery to use GSAP with MooTools only and GSAP selectors will fail(take a look at my first codepen).
I don't know if MooTools is doing it wrong or GSAP, neither is problem of Joomla because above code is single HTML file with similar behavior. My knowledge isn't that deep but I guess when we declare noConflict before MooTools, it takes control of more than just $ sign and affects GSAP in the process. GSAP developers should look into it.
Finally if anybody comes to this thread with same problem, I will recommend to use jQuery selectors. Thank you.