Upvote:3
Your newborn is a US citizen, and 18 USC Β§1185 requires US citizens to bear a valid US passport for entry into (and exit from) the US. Airlines know this, and will refuse to board her onto a flight to the US unless she has a valid US passport.
That she is a dual citizen of the US and another country is irrelevant. As a US citizen, the airline will apply the US-citizen rule cited above. Thus, the answer to "may she use her non-US passport" is "No."
If the passport application requires an original birth certificate, then send the only original you have with the application; if a copy is acceptable, send the copy. In the US, one may obtain for a minimal fee, usually from the Recorder in the County where the birth occurred, a new official copy of a birth certificate, which will be considered as an "original" for all purposes.