Does my ex (non-custodial parent) have to give me her address?

Most court orders have a provision that each parent is to provide the other with their current address at all times. You need to review your orders to see if this applies. If not, then there is no "law" that says it must be provided, although it is a matter of common sense and refusing to provide it is a red flag. You must follow court orders unless you get them changed. Considering the ages of your children, you should have brought a motion upon their return seeking to suspend visitation until mom proved she had a suitable place for them to exercise visitation. Otherwise mom can come to Arizona to exercise visitation. You can still bring that motion, and if you do, include in it that mom refuses to provide her address so you fear she remains homeless or otherwise without suitable accommodations for the children. The primary custodian has decision making authority over the day to day things what kids wear, what they eat, how they get to where they need to be, etc. If you share legal custody (and you probably do) then mom still has a say in major decisions such as education, medicine, and religion. Having primary custody does not allow you to violate court-ordered visitation terms. You need to ask the court to modify whatever orders no longer work. If you have Nevada orders, but no one remains in Nevada, you need to domesticate your case in Arizona (assuming the children have been there at least 6 months).

Which state governs your custody issue because it sounds like you need to petition the court for modification of visitation/parenting time due to the fact that the mother does not have stable living in which to provide for the safety of your children.

File to modify her visitation to supervised visitation based on your children living in a shelter on prior summer visit and the refusal to provide address. Seek an emergency order to keep the children in place with you until the modification request is decided.

All of your questions have to be resolved in the Court which entered the custody order, and I suspect they will not be pleased with her past performance.