You can switch who claims your daughter.
If you are both on the mortgage and deed and you both pay the mortgage and property taxes then you will need to split it based on how much you each pay. If only one of you is on the deed/mortgage than only that person may claim the deduction. You do not have to be HH in order to itemize your return and claim interest and property taxes. You do have to be legally liable for the mortgage and taxes though.
No, changing how you file or split credits (as long as you are eligible to do so) will not raise red flags.
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