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)?

Firmly but politely. "I love it that you are taking care of my child, but I am her mother and will make decisions on how she is raised". If you MIL doesn't take kindly and feels offended, then seek alternative child-care arrangements. I would not bring my husband into the picture as it might cause more friction.