I believe that, since your daughter was born in China with both Chinese and foreign nationalities, the "proper" course of action would have been to apply for a Chinese Entry/Exit Permit for her, instead of a Chinese passport. She can use the Entry/Exit Permit in combination with her foreign passport to exit China. And then once abroad, to return to China, you would apply for a Chinese Travel Document for her at a PRC consulate abroad. The Chinese Travel Document can be used in combination with a foreign passport to enter and exit China.
See this FAQ from the PRC embassy in Zambia (translated from Chinese):
I am a Chinese citizen. My partner is an X country national. Our child was born in China. Now we want to visit X country. What document
should the child apply for?
According to our country's nationality law, your child should be
recognized as possessing Chinese nationality. You can apply for
entry/exit documents from the public security department. For details
please inquire with the public security entry/exit administration
department of county-level or higher for your place of residence.
For example, here is the page from the Beijing public security bureau about applying for Entry/Exit Permits. (translated from Chinese):
Acceptance conditions
Hong Kong and Macao residents whose Mainland Travel Permit for Hong Kong
and Macao Residents was lost, damaged, or expired in the Mainland
and need to return to Hong Kong or Macao; Those where it is
inconvenient to leave the country with an ordinary passport,
including: 1) Children who have obtained foreign passports, one parent
is a foreigner and one parent is Chinese, and are recognized as having
Chinese nationality in accordance with the Nationality Law of the
People's Republic of China; 2) Children born abroad to parents who
have not settled abroad, who have obtained foreign passports, who
returned to China with the "People's Republic of China Travel Document",
and the Travel Document has expired and they want to leave the country.
However, the problem is that your daughter already got a Chinese passport. I don't know if this will prevent her from getting an Entry/Exit Permit. I don't know if there is a way to "undo" getting the Chinese passport.