i have altered your fiddle a bit, have a look Here
things to notice:
1 - you should select your jquery library on the left panel of jsfiddle.
2 - delegating event handlers by attaching them to document seem to work better for me
3 - using custom animation you have more control over the sliding
4 - set position:absolute for the sliding panel if you want it to work correctly
5 - when attaching the mouse hover to a menu item, always include the submenu as well or you will not be able to click the submenu since when you move the mouse out of the menu item the submenu goes off
if you have more questions, please let me know. -if my answer helped you, please consider accepting it :)