WOW-
you Mom is very sick, but you are unwilling to use Priceline or a consolidator because you won't get miles for your trip?

Let me get this straight. You are only willing to go to visit your sick mom if someone else pays for your ticket, and refuse to make it less expensive because you might not get miles on your trip. If you are being honest, then you priorities, in my opinion are way out of whack.

Who would care about accruing miles in a time like this?

When my grandfather was dying and I was living on student loans alone near the poverty level, I took a 3 leg flight on 3 separate airlines to visit him and comfort my grandmother. None of those airliens were my airline of choice, and one of those tickets was from priceline. It took me an entire day to get there, and I didn't get the miles I wanted, but I found a way to get there that I could afford, and I got there by any means necessary.

If you want to get there so bad, go on Greyhound to LAX and get a consolidator fare. Yeha, your trip will be long and unpleasant, but you'll get to see your mom for a very reasonable price, and isn't that what's important?