If you work remotely, the income is considered sourced where the work in performed. Therefore, the work you did remotely while in IA will be considered IA-sourced income. You will need to report any income earned while working in Iowa on a nonresident IA state return. Since you have no intention to change your state of residence, you will also need to file an AZ resident state tax return.
You will need to file as non-resident for IA (for your IA source income only - your IA remote wages). You will also need to file a AZ resident state tax return (for all income from all sources including IA wages). You will get a state tax credit in AZ for any IA state taxes that you paid on your nonresident IA state tax return.
You will want to work on your non-resident IA state tax return first. You will then take a tax credit from your non-resident AI taxes on your resident AZ state tax return. (Please note that you will only get a tax credit for your IA taxes up to the amount of AZ taxes that would have been paid if the income was earned in AZ).
Just follow the TurboTax guide when working on your states (remembering to do your non-resident state return first) and TurboTax will do all the calculations and credits to your resident states return
Here is additional information about filing in multiple states (select "see more answer" to view the entire attachment)
https://ttlc.intuit.com/replies/3300797