Hello!
This would be a customization beyond what we can offer here in support. We consider search to be a part of the plugin. It’s great that your theme offers search, too, but we provide search in the plugin and can only provide you with general directions for integrating the two. If you do choose to go down that road and either hire a developer or work on it yourself, we can provide advice and look over the code you share here in the forums.
GD uses custom tables, setup in such a way to make them scalable for maps with 50,000+ listings. This means that the tables are accessible via WP Methods but fields are not stored in the typical WP Custom Post Type manner (which is not scalable).
Take a look here at some search results to see what others have done in this regard:https://www.google.co.id/search?ei=GaILWoPGGYj9vgTqzJsg&q=site%3Awpgeodirectory.com+submit+search