I'm sorry about this diagnosis and its implications. I do want to tell you one thing in case it might help... My grandmother had "thick blood" and she went in and donated as often as they allowed. It actually helped her physically to do it, and she lived a very long time. I would mention this to your mom and her doctor. It's a very easy thing to do that doesn't require medicine.
Of course, if the Red Cross doesn't want this blood because of its properties, that is a different thing. The doctor might know this.
Long ago, leeches were used to help this. They didn't understand the blood properties, but they did know that it helped. Some hospitals actually use leeches now to do the exact same thing because it's more healthy than using medicines. (Medically grown leeches, that is.) Hard to imagine putting yourself through that though!
Good luck to your mom,
Dawn