Trip out of US to Europe using only UK passport + birth certificate [duplicate]

My daughter, who resides in the US, is about to fly to the UK for a brief trip. She holds both US and UK passports and citizenships, and has a NEXUS card.

Now, just before departure, we have realized that her US passport is inaccessible (it is with a distant relative).

Can she instead travel on her UK passport, then on her return successfully enter the US by presenting the UK passport, her US birth certificate and her NEXUS card? (I'm guessing they would be pretty unhappy, but not prevent her entering since it's clear she's a citizen.)

Assuming they will let her in, will she have any trouble leaving the country in the first place - given that the airline has her US passport number attached to her ticket?

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Can you use a certified copy of birth certificate for passport UK?

An original Certified Copy of an Entry of Birth (which is the official name for a replacement original birth certificate) is fully accepted by the passport office. This is what is referred to as an Original Birth Certificate, and what is supplied by Vital Certificates.

What documents do I need to travel to Europe from the US?

A U.S. passport (with applicable visas, if needed), valid for at least 90 days beyond your intended date of departure from the Schengen area. Note: Border officials often assume you will stay the maximum 90 days, even if this is not your intention. Sufficient passport validity for each country you will visit.

What documents do I need to travel to Europe?

Travel documents within Europe You will need an ID card or passport if you are travelling within the European Union. And not just when you cross a border (for example, via an airport). You must also be able to show an ID card or passport if you are staying in a European country. Some countries also require a visa.

What documents are needed to travel abroad?

Passport, Travel Visa and National ID Card Proper identification is the foundation of international travel. As a result, you should ensure to always have an official identification document with you. You can even consider having multiple documents such as your passport, national ID card or driver's licence.

Exodus: I tried to fly to London on a fake passport - BBC News

Sources: Stack Exchange - This article follows the attribution requirements of Stack Exchange and is licensed under CC BY-SA 3.0.

Images: Gustavo Fring, Ethan Wilkinson, vectors icon, Samson Katt