All money in an HSA is treated the same way, whether it comes from an employer contribution, a payroll deduction, or an after-tax contribution. If you withdraw money for a nonqualified purpose, it will be taxed as ordinary income plus a 20% penalty.
Because your daughter is married, she cannot be your dependent if she files a joint return with her spouse. If she files a separate return from her spouse, you would be able to claim her as a dependent for medical purposes only if you provided more than half of her support.
