Can anybody let you know that this really is working?

RewriteRule ^update_my_account/([0-9]+)/([0-9]+)/?$      /index.php?page_id=$1&updated=$2 [L]

What area of the URL is $1 and $2 based on?

$1 means first group anything matched up beginning with ([-9]+) inside your rewrite regex and $2 is second ([-9]+).

$1 consists of whatever is matched up through the first expression inside brackets ([0-9]+), and $2 consists of whatever is matched up through the second ([0-9]+).