@Dan Oliver
Your proposed plan to spend most of your time in New Mexico creates a complication. Since different states have different definitions of a resident for income tax purposes, it is possible to be considered a resident of more than one state at the same time. There is also a concept called domicile, which is not the same as residence. You can have only one domicile.
As long as your family remains in Arizona, and you consider that your home, your domicile is in Arizona. Arizona considers you a resident for income tax purposes if your domicile is in Arizona.
But New Mexico considers you a resident for income tax purposes if either "Your domicile was in New Mexico for the entire year or You were physically present in New Mexico for a total of 185 days or more during the tax year, regardless of your domicile." From your description of the arrangement that you are considering, it seems that you would be physically present in New Mexico for at least 185 days during the year. That would make you a resident of New Mexico for income tax purposes.
As I said, it is possible to be considered a resident of both states at the same time, and it looks like you would be in that situation. That means you would have to file resident tax returns in both states. I don't know how the credit for tax paid to another state works if you are a resident of both states. The fact that your wife is a resident of only Arizona might further complicate the situation. You should consult a local tax professional to find out how your plan would be handled.
You can find the definitions of a resident in the tax return instructions for each state, which you can download from the following links. The instructions also discuss domicile.
Arizona Form 140 Booklet
See "Determining Residency Status" on page 2 (page 8 of the PDF).
New Mexico PIT-1 Instructions
I can't find a direct link to the file. Go to the Forms & Publications page and click Income Taxes > Current Year Tax Forms > Personal Income Tax > Personal Income Tax Return Forms. Then click "Open File" for the PIT-1 instructions.
See "Definitions" on page PIT-1-4 (page 4 of the PDF)
