A check for if is parent page, if has children, if has grandchildren

I have one default page template that I wish to use for two scenarios. I'd prefer to use only one page template for the sake of simplicity for my client.

Here's what I'm trying to accomplish:

if parent_page OR if child-page without children {
  display full-width-layout
}
if child page with children or if grandchild page {
  display sidebar-menu-layout
}

Is this possible?

This is what I've tried so far:

if( is_page() && $post->post_parent > 0 ) {
  //display sidebar-menu-layout
} else {
  //display full-width-layout
}

It works so far as on top level pages, it displays full-width-layouts. But, what can I do to make sure that the sidebar-menu-layout is displayed on child-pages with children and on grandchile pages only? And for child-pages with no children, to display the full-width-layout.

Thanks in advance. I'm sure it has a simple solution, I'm just relatively new to WP so still trying to figure out what can and cannot be done.