You can request through DCSS for the debt cancelation. If the debt was collected through DCSS in regards to aid then that is the county's money, and they make a literal fortune every year from the collection of child support. If the debt is from enforcement of child support from the other party, then you need a court ordered stipulation that addresses that debt.
It really depends on whether this judgment was signed and adopted by the court. If there is an issue of what the judgment should say, then what was orginally agreed to in court should control. If he took money out of a joint account then that is a violation of the ATROS and you can go to court and get relief from that.
First off I am not a Arizona attorney, but if it involves child custody, UCCJEA is going to apply accross state lines. All you have to do is to file with the court to register the out of state order, assuming you lived there for 6 months and go from there.
Probably your best move would be to go back here to California and request a change of venue to your new state. Given that you don't know where she is that would be somewhat tricky to serve her. Put any move would probably involve you coming back to California to change the court.