You can check if current category is a child of blog category with cat_is_ancestor_of() function or term_is_ancestor_of(), or maybe better, use in_category(), as you are currently doing, but checking child categories as well.
add_filter( 'single_template', 'get_custom_cat_template' ) ;
function get_custom_cat_template( $single_template ) {
// You want to filter only template for single posts of default post type
if( is_singular( 'post' ) ) {
$post = get_queried_object();
// Replace '3' with the ID of the 'blog' category
$child_blog_categories = get_term_children( '3', 'category' );
if ( in_category( 'blog', $post ) || in_category( $child_blog_categories, $post ) ) {
$single_template = locate_template( 'single-blog.php' );
}
}
return $single_template;
}
Anyway, I think that if you see yourself creating a category of posts to manage posts whithin that category in a different way, you may want to check out custom post types.