Hi and welcome to iMore.
Go to Settings > Phone >, Blocked and press Edit to unblock a number. I'm not sure what you mean about yoru wife having the account details. You don';t need to log in anywhere to block or unblock a number if it has been done on the phone.
If it has been blocked via your carrier then the only way is to contact them directly. Traditionally they will only speak to the account holder and if they won't speak to you, you will need to ask your wife to do it.