People who are married can file a joint tax return even if they do not live together or in the same state. Happens all the time. People file state returns for states where they do not live because they have income from that state. Where you file state taxes if a factor in determining residency, but not the only one.
In this case, the mother living in Alabama might not have any need to file in Alabama if she has no income. She could still be an Alabama resident if she lives there, registers her car, registers to vote, gets a library card, or does whatever else the checklist requests. She’d have to check what the requirements are for residency for tuition purposes. Those might be different than being a resident.
States can set any rules they want. My nephew had instate residency in 3 states. Colorado gives instate rates if one parent live in Colorado, and for my nephew his father does; no requirement to claim him on taxes or show support. He had instate in Florida because he graduated from high school there. His mother moved to CT, and after a year he gained residency there.
Other states set much stricter rules and students can gain residency only after 2 years or may never gain it.