Without wanting to state the obvious, you purchased the fare knowing the ticket was non refundable and subject to fare difference and change fee at the time of purchasing the ticket. These will have been clearly visible during the booking process or advised to you if making the booking via a call centre. Had flexibility been an important factor when purchasing the trip then I'd like to think you'd have purchased a ticket with more flexibility rather than one based purely on price.

While they're entirely plausible reasons that you find yourself wishing to change, I personally don't think it's reasonable to expect the airline to waiver the charges under the circumstances to which you've explained.

Travel insurance may allow for cancellation depending on the wording of your policy. For example some policies allow for cancellation based on the health conditions of a family member on which the trip depends (not necessarily the same as the person who's insured.... the devil being in the detail - mine has this for example). This may require a doctors note from your family members specialist advising against them having visitors due to their medical condition. They may not be prepared to provide this of course in which case you'll be stuck proceeding, however if they do then this may give you an extra avenue of getting a full refund on your otherwise non-refundable ticket via insurance in this situation before starting over with a brand new ticket for the required dates.

All things considered it may just be far simpler to just stump up the fare difference and chalk it up to experience.