Hi guest! I have an infinite respect for you and your family. I know how hard it can be for loved ones when they would do anything to help, but don't know how. It is frustrating and upsetting for the bulimic, too, as we all don't want to live like that...we want to get better...but if we can't figure it out, we don't know how other people can help us either.
When reading your post, I too had warning sirens going off when you mentioned that your mother gives your sis daily food money. This can be extremely hard for a bulimic. Whenever I've lived by myself, I find it really difficult to buy the 'right' foods. I usually tried to buy/eat healthily, but I had no concept of what was a good amount to have, that usually I didn't get enough. This would lead me to buy lots of food the next time.
As your mother is on a limited budget, and obviously has a more realistic view of 'normal' eating, it would be better all around if she bought and cooked for both of them. Talk to your sister, and find out what her 'trigger' foods are, and what she doesn't mind keeping down. Then try not to have the trigger foods around the house. But if she's throwing up everything, this will be a little useless I guess.
Also, it does help to get out of the house as much as she can. Try doing things with just the two of you (she may be anxious to be around others right now). Go for walks, go to a movie, go window shopping, do some volunteer work together, take up a hobbie together. The more 'fun' things in her life, the easier her recovery will be.
Biggest thing though, as the others suggested, is getting some sort of professional help. Are there any live-in eating disorder clinics in your area? (They're normally very expensive, though). How about showing your sister this site? Maybe it would be good for her to give herself a code name and talk to people who understand? (Though we're not professionals!)
Also, I was glancing through old threads in the bulimia forum a few days ago, and came across one for friends/family of sufferers, and it has a link to a site specifically for people like yourself. I haven't checked it out, but I figured I'd give you a link to the forum, and you might have a little squiz.
http://www.psychforums.com/viewtopic.php?t=5688
Good luck. You're an amazing individual!