My first thought was that there's no way you'd need your ex's permission to move closer to him.
However, joint legal custody requires you to agree on major parenting decisions or go to court to work it out. We're talking about a change of schools here. Schooling is generally considered a major parenting decision. It probably is something you should try to work out. Realize though, that if you are unable to agree and you have to take it to a judge, it will be a quick decision in your favor.