Hi,
I have check your code(html/css) and i have found out that there are some specialized instance for the navigation to work. Unfortunately. the plugin has no control on this instance. But you can try this steps.
After activating the plugin, open you theme's main style, which usually named as "style.css" and add this code on the bottom.
.nav-menu {
position: inherit !important;
}
.nav-menu .children {
z-index: 999 !important;
}