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You'll have to get a consular report of birth abroad from the Department of State, which will act to replace the birth certificate as evidence of your daughter's citizenship.
That is through the U.S. Citizenship and Immigration Services.
I do not work in immigration, so I do not know the exact paperwork she needs. That is a question for an immigration attorney. I'm just a military law attorney that knows that those born abroad have to apply, with immigration, for that certificate to show that she is a citizen.
So, she needs to go to a local immigration office, ask them what paperwork she needs to bring, and then request that document.
Once she has it, no she should not have any trouble with immigration.