The question you are seeing about 'how long did she live with you?' relates to the Earned Income Credit, which only the custodial parent can qualify for. The custodial parent is generally the parent with whom the child lived for the longer period of time during the year. Total your number of overnights with your daughter and enter the appropriate number of months on this question.
However, even if you are not considered the custodial parent for tax purposes, you can still claim her as a qualifying child dependent for the child tax credit or credit for other dependents.
Click the link for more detailed info on Splitting Child Deductions for Divorced or Separated Parents and don't worry, TurboTax will take care of Form 8332 for you.
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