Genesis – Adding custom hooks to display secondary navigation

Yes. you can do that.

function my_custom_footer() {
    ?>
    <div class="site-footer-logo">
        <img src="https://wordpress.stackexchange.com/questions/179519/<?=get_stylesheet_directory_uri();?>/images/my-logo-small.png" alt="My Logo Small" />
    </div>
    <?php do_action('my_own_hook'); ?>
    <p>Copyright &copy; <?=date('Y');?>, my-url.com.</p>
    <?php
}

add_action( 'my_own_hook', 'genesis_do_subnav' );

function genesis_do_subnav(){
    wp_nav_menu( array( 'theme_location' => 'secondary-menu' ) );
}

You also can directly add:

</div>
<?php wp_nav_menu( array( 'theme_location' => 'secondary-menu' ) ); ?>
<p>

Note that secondary-menu here should be registered.