Your daughter will be a Texas resident until she changes her domicile to another location. Your domicile is where you live, where you have a drivers license, where you receive mail, where you have your phone, and where you are registered to vote.
As you can see, this is not a cut-and-dried definition, but one way of looking at it is - where do you tell your friends that you live? And where is the place you are returning home to?
As Kris said, it is common for college kids to maintain their parents' domicile, until such point as they go somewhere to "stay" - it does not have to be permanent, but to change your domicile requires an effort on your part.
As for filing other states, a young woman in her situation might file a nonresident DC return in order to recover her withholding - your (I mean, her choice).
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