On the registration form, just indicate that you do not want to be on the same team and your child will be removed as a core player from that team. Your child will be placed in the Player Pool for random assignment to a new team. NTSSA rules require that children be assigned to teams in a fair manner.
As long as there are more than two teams/coaches in a division, you may request that your child NOT play for a particular coach by designating this in the appropriate area on the registration form.