I'm going to dictate where my brothers children go to school
Why would you tell them which school to go to?
I want to be more involved in their lives.
I appreciate you wanting to be involved your niece's and nephew's lives, but there education is really a decision their parents need to make for them. Perhaps, you can just give your advice on where they should go to school.  I think if you try to force something on them, they'll probably just laugh at you and ignore you completely.
What do you know? I'm their uncle and they'll listen to me! I want to get rid of their current school and make them go to my private school.
They aren't your children and you have no right to tell them where to go to school. Just leave that decision to your brother and stay out of it.