How can I get some of a posts meta data whilst it is still inserting?

Maybe you can move all the logic to added_post_meta & 'updated_postmeta' hooks.

add_action( 'added_post_meta', 'update_carnews_adverts_aprent', 10, 4 );
add_action( 'updated_postmeta', 'update_carnews_adverts_aprent', 10, 4 );

function( $meta_id, $object_id, $meta_key, $meta_value ) {
  if ( $meta_key !== '_wpcf_belongs_carnews_id' || ! is_numeric($meta_value) ) return;
  $post = get_post( $object_id );
  if ( $post instanceof WP_Post && $post->post_type == 'carnews-adverts' ) {
    $parent = get_post( $meta_value );
    if ($post->post_title !== $parent->post_title || $post->post_name !== $parent->post_name) {
       $post_update = array(
          'ID'         => $post->ID,
          'post_title' => $parent->post_title,
          'post_name' => $parent->post_name
       );
       wp_update_post( $post_update );
    }
  }
}