AA's policy is to consider ticket refunds and change fee waivers/refunds in the case of critical illness of a close family member. Documentation and justifification must be submitted through regular refund channel. I suspect a change fee incurred to extend a visit with a qualifying relative would receive favorable consideration for a refund, but it remains at AA's discretion.

I'd prefer not to link the policy as it's on our travel agent reference website. However, it's publicly searchable and accessible. Try "aa critical illness exception request".