You can't choose how you want to prepare and calculate your returns. TurboTax uses federal and state tax law to prepare and compute taxes. Each state has its own set of specific rules. Your resident state taxes you on 100% of your income - always. And as @RobertB4444 explained above, your resident state will issue you a credit on your resident tax return to remove the impacts of double taxation.
Enter your W-2 as it appears. Then prepare your NY non-resident return first, before your AL resident return. This will ensure TurboTax applies the credit for taxes paid to another state correctly. When you go through the NY nonresident return, only allocate the amount that was earned while you were physically in NY. There is an article below that provides further details on filing returns in multiple states.
Multiple States—Figuring What's Owed When You Live and Work in More Than One State
Do I have to file tax returns in more than one state?
Why would I have to file a nonresident state return?
How do I file a nonresident state return?
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