College credits and the Child Tax Credit have nothing to do with Itemized or Standard Deduction. They are completely separate. So you can claim both credits (if eligible) even when you use the Standard Deduction.
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As for any potential ability for your daughter to claim "independent", no. If she is ELIGIBLE to be claimed as a dependent, she can NOT say she is 'independent'. She would need to say that she CAN be claimed as a dependent.
However, some of your comments are a bit confusing. You said she was 100% dependent, which sort-of implies that she has no income at all. But you also commented about 'filing' her independently, which seems to imply that she does have income to file a tax return.
As a grad student, how old is she? If she turn age 24 (or older) in 2020, then you would only be eligible to claim her as a dependent if her income is below $4300 (there is no income limit if she was younger than age 24 at the end of the year).
