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)?

Listen without interrupting and filter without having to cut them off. But if they get too pushy gently remind them that although you are grateful for their opinion (since they raised such a good person: your spouse), there are certain things that can only be decided on by the parents. Make them feel valued and respected and always speak to them with love but firmness. :)