To update an existing relationship field to add a value you first need to get the existing value without formatting and then add the new post ID to it.
// get current value
$value = get_field('relationship_field', $post_id, false);
// add new id to the array
$value[] = $inserted_post_id
// update the field
update_field('relationship_field', $value, $post_id);
To delete existing values in the current post
delete_field('some_field', $post_id);