From what you have written, it appears that the non-custodial parent can sign up your children for sports and horseback writing. The real issue is whether or not under the presumed child custody order that you have is whether or not she is allowed to do so.As such, I suggest that you read all child custody orders between you and your childrens' mother to see if she was allowed to do what she did nor not allowed to do what she did. If the court order is silent on the subject, she most likely was allowed to sign up your children for what she did.