Yes, you do need to get her UK passport. If she only has a US passport, she will only be let back in to the UK as a visitor, not a UK citizen. In order to show she has the right to live in the UK, she would either need a visa in her US passport or she needs a UK passport.
You must use her US passport to enter the US, as it's illegal for her to enter on a UK passport. Then you use her UK passport to enter the UK to show she is a citizen and has the right to live here.
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