The "kiddie tax" is not based on being the parent's dependent. It's based on age (under 24), student status (full time) and earned income (the student's earned income is less than 50% of his support).
Education stipends are not typically considered earned income for tax purposes. Stipends are either taxed as other income or (less frequently) scholarships.
Beginning in 2018, the kiddie tax is applied at trust rates, rather than the parent's tax rate. So, yes, you are technically subject to the Kiddie Tax as high as 37%. See https://www.marketwatch.com/story/new-tax-law-makes-dreaded-kiddie-tax-more-expensive-2018-09-24
EDIT (1-21-20) The new (2019) tax law reverts kiddie tax rates back to parent rates.
