I've been in the same boat., so no judging here. Your life can't stop. In terms of the change fee, I believe AA has waived the change fees for tickets (check the site for the details), so I don't think you have to worry about that.

On the travel insurance, when did you buy the ticket? This is important because travel insurance has pre-existing condition limitations unless you buy the insurance within so many days of making your first payment on the trip. Since your mother is already ill, they may not pay out any benefit.