Which Parent Rules?

My ex wants our son to go to private school, but I want him to go to public school. Who decides?

If both parents have joint legal custody, then they should consult each other on matters of major importance, such as which school the child should attend. But the parent that has primary physical custody is the one who has the final say.

There are Different Types of Custody

My daughter is 16 and I share joint custody with her father. She lives with him, but wants to live with me. Can she do so without her father granting permission?

You need to examine the wording of your divorce decree. You may need to consult a lawyer, as sometimes the terminology used to describe different types of custody is not self-explanatory. At a minimum, I would not take it upon myself to move the child unless you had physical custody or the father agreed.