Load many media grids (image galleries) via ajax on the same page

I have many image galleries, each gallery is a media grid and has its own page.
I have 3 main galleries and the rest are children of these 3.

I want to show the 3 main grids by default on the main page.
Next to each grid, I want a menu that fetches the sub-galleries nested under each main gallery.
When you click on a child menu item, I want to load via ajax the gallery that corresponds to that menu item.

Something like this can be found at this website
http://old-sinks.com

For example, “Bowed” is a child item of "Bathrooms Sinks"
When I click on it, a different image gallery appears in place of the main gallery under “Bathrooms Sinks”

Is there a plugin (paid or free) that would allow me to achieve that without over complicating the process?
Is there a better way to do it? Maybe a Portfolio grid with filters if I can hide “ALL” posts from the main view.