How do you let you mum-in-law know that you will be calling the shots on the upbringing of your child (without sounding rude)?

Sit her down and tell her respectfully that, as a parent of your child, you want to bring them up your own way. It is, after all, your right as their parent. Not that she deserves it, but as a sign of respect give her a list of reasons why you've decided to do it. And the truth of the matter is she has no say about this, because a child's responsibility falls on their parent first and foremost. Hopefully your in-law is a reasonable human being and will see reason in your choice.