I'm having the same issue with not being able to select child themes. It looks like the problem is caused by relying on the "template" attribute of the theme instead of the theme name - which is problematic because a child theme has the same template as its parent. For instance, line 159 of md-admin/functions.php
<option name="theme_template" value="<?php echo $mobile_theme['Template']; ?>" <?php if($mobilemeta->theme_template==$mobile_theme['Template']) echo 'selected="selected"'; ?>><?php _e($name); ?></option>
Setting the value to $mobile_theme['Template'] means that a parent theme and its children will have the same value in the dropdown menu.
I think the solution is to separate template and stylesheet, this is why WordPress has separate values for these in the wp_options table.