In Arizona can a 17-year-old living in an emotionally abusive environment legally choose to live with the non custodial parent who pays child support or with a legal guardian?

Not legally. The parent who was awarded custody has legal rights over a minor child until the child reaches the age of majority as defined by state law (Arizona AOM is 18) or a court rules otherwise. However, when an older child is capable of understanding the consequences of leaving the custodial parent's home and moving in with a non custodial parent (not a friend or relative) authorities cannot force the minor to return to the custodial parent without a court order. The custodial parent would have to sue the non custodial parent in family court to have the custody order enforced and the minor returned to his or her custody or remanded to juvenile authorities. The necessity of a court order does not apply if the minor crosses state lines or moves in with an person other than the biological parent (grandparents, adult siblings, friends, significant other, etc.) A guardian can only be appointed if the parents have voluntarily relinquished their rights to the child or the court has permanently or temporarily terminated parental rights.