I have a different perspective.

A non-shareholder employee is not Self-employed. A non-shareholder employee is just an employee, period. Being an Adult, has no bearing. Being the Child of a shareholder of that employer, has no bearing.

Reimbursing this person for their own costs for health insurance is a Taxable benefit, as a Bonus, justified in the amount as against the cost. Getting this as a credit or deduction on the 1040, not a Sched C, is not related to anything "Self-employed."