For the money to be considered to be compensation, it would have to be reported on the child's Schedule C as income as self employment. Payment to a child for doing normal household chores would not typically be considered to be income from self-employment. Even if $2,000 was reported as self-employment income, some amount would go to self-employment taxes so the Roth contribution would be limited to less than $2,000.
Unless corrected by a return of contribution before the due date of the child's tax return, the excess Roth IRA contribution must be reported and the 6% penalty paid with the child's tax return. If by April 15 the child files the tax return or requests a filing extension, the deadline to obtain a return of the excess contribution is extended to October 15.
