Can my exwife enroll my child in private catholic school without my consent?

I am from MA and have shared legal custody of my children with my exwife. I have three children. My oldest two children attend the public school. My youngest child was enrolled last year in Kindergarten without my consent at a private catholic school. I am trying to get my youngest child to attend public school like my other two children. My wife does not work (basically she does so under the table to hide her money in court). I pay her $450 weekly as court ordered for support. She is always telling the courts that the weekly support isn't enough even though it is decided by the MA child support formula. My issues is that we are not in the financial position to send my child who will be in grade 1 to private school and also my other two children attend the pubic school.