Working on the same thing; ran into a slightly different problem. Everything drags and drops just fine, but when I go to save the menu I created, all of my "child" pages automatically shift back to the left. Any ideas why?
Have deleted my menu and started over. No luck. Under Pages, all my pages are correctly placed under their parent page. I've tried making them all top level pages here and then designating them as child pages under Appearance > Menus. Also tried deactivating all (2) of my plugins as another post recommended. Doesn't work.
Any help? I'm using the Weaver II theme. I not tech savvy at all, so anything involving code would need to be explained as if talking to a 5 year old: "Click the mouse on button X. Copy this. Paste it here. Press enter..." :)