Search child pages from a specific page parent

I have no idea if this will work, but couldn’t you reference the post_parent in the query args?

function SearchFilter($query) {
if ($query->is_search) {
    //$query->set('post_type', 'page');
    global $post;
    $query->set( 'post_parent', $post->ID );
}
return $query;
}
add_filter('pre_get_posts','SearchFilter');

Again, completely untested. I’m not terribly familiar with using $query->set().