Use javascript to add "hover" class to your menu item.
Current CSS:
.showDropDownMenu {
display: inline-block;
}
New CSS:
.showDropDownMenu, showDropDownMenuHoverEffect{
display: inline-block;
}
When the nav button is clicked use javascript to walk your menu and add the "hover class (showDropDownMenuHoverEffect)" to the menus you want to display. When the nav button is clicked again use javascript to remove the "hover" class.