I also have a green card and was told that I only need three months validity to get back into the US with my green card and UK passport. My daughter, who is a dual citizen, was told last year when she went through passport control at LHR she could enter the UK on an expired UK passport if she wanted as they couldn't deny her entry if she was a citizen. I really think your daughter will be fine but maybe make some phone calls to put your mind at rest.