You must secure agreement of the child's mother to move or a court order allowing you to do so. You must file a motion for leave to remove your daughter. Hire an experienced attorney and begin to together to prepare your case to prove that it is in your child's best interests to move. Your child's mother has the right to try to prevent you from moving.
Yes she can keep you from taking your daughter outside of Illinois because that is our law. Unless she agrees or you have a court order saying you can remove her from the state you cannot. Hire a lawyer to file a removal case. The parent child relationship is what the public policy is protecting. You will need to prove removing her from Illinois to the new state is in the child's best interests.
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judy and peggy said it correctly and succinctly. removal cases are not easy, quick, nor inexpensive. i doubt you could do this without a lawyer. get one familiar with removal. ask if the lawyer knows about the collingbourne and eckert cases from the illinois supreme court. if not, get another lawyer. you read the cases to see what must be proven to succeed in a removal case.