Yes, you may claim expenses paid for your non-dependent child. From publication 969 (HSAs):
Qualified medical expenses are those incurred by the following persons.
You and your spouse.
All dependents you claim on your tax return.
For this purpose, a child of parents that are divorced.....is treated as the dependent of both parents whether or not the custodial parent releases the claim to the child's exemption.
Choose "self only", as you are not entitled to the higher contribution limit.
