What can I do if my ex will not let me know the address of where my kids and her live?

How much money do you have? How much time? You could hire a private eye to tell you what is going on. You could follow her and see what the deal is. If she is homeless, you should probably file a petition to modify custody so the children have a safe, stable place to stay.

Unless the court has ordered that your ex-wife is permitted to keep her address and that of your children private and expressly authorizes her not disclose it to you, there is nothing I can find in the Utah Code that mandates that your ex-wife must notify you of where she resides when she relocates. But do not lose hope quite yet. It is likely that your Decree of Divorce contains a provision like this: "Each parent shall provide the other with the parent's current address and telephone number, email address, and other virtual parent-time access information within 24 hours of any change." If that is the case, then if your ex wife does not notify you of a change in her address or other contact information as ordered, you can file a motion with the court asking to have her held in contempt and sanctioned for failing to comply.