My ex-wife has sole custody of our 3 children. My 13 year daughter wants to move to my house for school. What rights does either she or I have in this matter?
Your daughter has no right to initiate court action to allow this move. You have the right at anytime to file a petition to modify custody. The issues related to the grounds for a court to hear such a request are first determined by the the length of time since the last custody order was entered. If in fact the last custody order was entered less than 2 years ago you will need to file specific documents with your petition alleging that the child is in serious endangerment, see state law 750 ILCS 610. The fact that your child wants to live with you would not meet this criteria and thus the court would not even take the opportunity to listen to the potential positive points as to why she wishes to live with you.
You have the burden to file a petition to modify custody -- a court may take in consideration the wishes of a 13 year old. However, just because she wishes to move does not mean that will be the determing factor. A court has to consider what is in the best interests of the child and that will be many different factors. Please consult an experienced family law attorney in your area.