How to extend a view plugin style implemented by another module?
First you need to have a my_module.views.inc, which can have basically the same contents as http://drupalcode.org/project/leaflet.git/blob/refs/heads/7.x-1.x:/leaflet_views/leaflet_views.views.inc, but with changed names.

You can leave the handler the same, in which case you need to leave the path the same too. Otherwise you can create your own hadler in my_module_views_plugin_style.inc along the lines of

class my_module_views_plugin_style extends leaflet_views_plugin_style {
   // ...
}


You then only need to define any methods that you want to modify: 

function option_definition() {
  $options = parent::option_definition();
  // your changes here
  return $options;
}


You also need a theme file. If you are modifying the display at all, you probably need to just copy the theme file over from the dependency, and change the 'theme' line in my_module.views.inc.