Legally move from AZ to SD.
You can't just get a SD DL, register vehicles etc. and still be legal residents of AZ just to avoid MH registration fees.
IF you are going to become residents of SD and travel....
Set up your new legal SD address via a mail forwarding service (can do that on-line). For DL's you will need to physically apply in person with the proper documentation. And sign an affidavit that SD is your only state of residency.
Course as SD residents your Medical Coverage/Insurance, vehicle insurance will be based on your SD address.
So are you ready to 'move'?