How can I get an intervenor off of my case?and what is the intervenor legaly allowed to do in my case?

If the grandmother has been permitted to intervene in your case, she is now a party, and is able to ask for grandparent visitation pursuant to A.R.S. 25-409. In order for her to ask for grandparent visitation, she had to have asked the court to permit her to intervene in your case because she was not a party to that case already, and you have to be a party in order to make a request like grandparent visitation. You cannot get her "off" of your family court case. You can, however, demonstrate to the judge why your child should not have contact with the grandmother. You will have to prove to the court that it is not in your child's best interest to have contact with the grandmother, and it is going to be insufficient to simply tell the court that because the grandmother raised your ex-husband and your ex did terrible things, she should not have visitation with your child. Also, her not ever being there to support you or your child in the past is not a reason to now deny her contact. I recommend that you consult with an attorney who has experience in grandparent visitation cases so that you can obtain more advice about your particular situation.