Besides, the mother is a commoner.
This statement is incorrect. She is the wife of a peer (Prince William is the Duke of Cambridge) and, as such, is not a commoner.
And, before you state that she was *born* as a commoner, I should point out that so was her husband. In the UK, a commoner is someone who is not a peer or the monarch (or a woman married to a peer/the monarch). Prince William did not enter the peerage until he was created the Duke of Cambridge on the morning of his wedding day.
Very few people are born peers (only those whose fathers who were peers died prior to their birth). Everyone else is born a commoner.
The Wolf