You are correct, if you are the custodial parent and all the rules for a qualifying child apply, then you can still claim Head of Household even if the other parent is claiming them. If TurboTax is giving you single instead of Head of Household, then it is likely based on a question you answered that would not allow you to be head of household.
Go back through your answers in the personal info section for both you and her to be sure that you have properly answered all of the questions. Pay close attention to the wording for the questions asking if you paid for over half of the household expenses and if your daughter paid for more than half of her living expenses.
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