The Kiddie Tax is based on unearned income of the child, not earned income like wages.
If the child has unearned income, interest, dividends, capital gains, of over $2,100 then they have to complete IRS Form 8615 - https://www.irs.gov/forms-pubs/about-form-8615
Since the child has earned income they have to file their own tax return, reporting both their earned and unearned income.
