Here is a basic idea:
Any page where the page parent ($post->post_parent) is 0, it means the page is a top level page. If any other value exists, the page is a child of another page. This value is the ID of the page that the specific page is a child to.
With the above information, we can calculate if the page is a child or a granchild using get_post and the returned WP_Post properties.
You can try the following: (CAVEAT: Untested)
if ($post->post_parent === 0) {
//Do something for post parent
} else {
$q = get_post($post->post_parent);
if ($q->post_parent === 0) {
//Do something for direct child
} else {
// Do something for grand child
}
}