Just as you should carefully review the contract you have, you should review your travel insurance policy, apparently through a Citi card. Does your Citi policy cover your need to cancel in order to take care of someone who is not traveling with you? If not, then your Citi benefits will not help either.

As to TK, it is TK. Some carriers have specific contract provisions which cover situations such as this. You are not ticketed on one of those.

Threatening a lawsuit is the worst approach unless you can point to a contract provision TK has violated.