“1. If Alabama taxes income based on where you live and/or where you work, why don't Alabama residents that work in the state have to pay double?”---->UNLESS full year residents of AL state have income that they earned in another state, they need to pay tax to ONLY to AL on their AL source income.However, as long as full year residents of AL have income that they earned in other states, thren they must file AL and other state returns. They can claim taxes that they paid to other states on their AL returns.
“2. I have to report my Tennessee income to Alabama to determine the % Alabama income to apply deductions. How can Alabama require a non-resident to report income to them?”---->Since there is no State Tax Reciprocal Agreement between AL and TN, your spouse needs to file her AL return as a nonresident of AL and can claim her tax that she paid to AL on her TN return. Your spouse needs to file AL return as she has AL source income that she earned in AL. So, she files her AL return as a non-resident of AL and file her TN return as MFJ with you.