US Citizen Baby born abroad China, Visa Questions???????????

Hi, All. My baby daughter is borned in China. Now she has both US and China citizenship. We reside in China, and plan to travel back to the States once a year for vacation. I was told that for the first time, my daughter goes back to the States, she has to obtain something called a Proforma Visa. Is that True?
And If she exits China with her US Passport, can she come back to China with her Chinese passport?
Your advise is greatly appreciately.