The rules for New York State are that you are considered a full-year resident if your domicile was in the state for 184 days or more. That's the first six months of the year. California has the same rule.
So in order to do this return correctly you need to first do the California return as a part-year resident first. That allows you to adjust your income in California since your daughter only resided there for about a third of the year.
Then you will do the New York return as a resident. Your daughter will be taxed on all of the income that she made for the entire year but she will be able to take a credit for the tax paid to California. That will reduce her taxable income in New York.
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