I'm terribly sorry for your situation.
One situation where AA will offer refunds is when there is a schedule change of more than an hour, so I would be on the lookout for that (especially if you booked a really long time ago). Also, if there is very bad weather (not unlikely in the winter), and AA issues a travel waiver, they may be willing to issue a refund rather than rebook you on other flights; travel waivers are generally issued (and posted on AA's website) a few days beforehand.
AA will also issue refunds in the event of a death of a traveling companion. While this is not a death, you might be able to convince a sympathetic agent that this situation is effectively the same. While one of your traveling companions isn't technically dead, he's effectively dead because there's absolutely no way that you can travel with him. You will likely have to produce some sort of documentation in this case, though.
Other than those scenarios, AA likely will not issue a refund. I might try your credit card company, especially if it's one you've had for a long time, and see if they would be willing to issue a chargeback, given the circumstances. At the least, they might be willing to allow you to defer payment on that charge without interest while you sort out your situation.