From what you described, it sounds like you might need to use a custom walker for the wp_nav_menu
call. To create a custom walker that modifies the wrapper for dropdown lists, start with this class:
<?php
class wpse_112127_walker extends Walker_Nav_Menu {
function start_lvl( &$output, $depth ) {
$indent = str_repeat("\t", $depth);
$output .= "\n" . $indent . '<div class="dropdown"><ul>' . "\n";
}
function end_lvl( &$output, $depth = 0, $args = array() ) {
$indent = str_repeat("\t", $depth);
$output .= "$indent</ul></div>\n";
}
}
Then, use your walker in your wp_nav_menu
call:
wp_nav_menu( array( 'walker' => new wpse_112127_walker ) );
This code should hopefully get you started on using a custom walker for your use case. Let me know if you have any difficulties/questions!