I think this 'fat bastards' comment needs to be nipped in the bud so we can just get on and offer support for the lady and her daughter.
What's the difference between 'I'm such a fat bastard today!' and 'I'm such a fat cow today!'? Just a matter of how comfortable one is with curse words?
Also, I think the way it was originally used was fine. The woman who used it did so in relation to people who stuff themselves and kill themselves intentionally that way (because they don't watch the calories). In other words, someone couch potato who eats solely iced doughnuts all day long and whinges they can't lose weight. Personally, I think that's perfectly reasonable to be scolded for. The adage 'eat less, more more' isn't hard to comprehend. Look at the majority of diet programmes - those people are totally delusional as to what they eat and how much.
Before I was in fully-fledged anorexia, but still on the downhill slope, I went to my GP. It was a deliberately concealed cry for help as I purposefully brought my food diary with me and was at pains to tell him about it and said that he could look at it. Thing were recorded in freakish detail - '8 sips of milk, last sip rather large gulp though', '3 squares chocolate, but may have dropped some shavings on floor'. The guy, leaning back in his chair the whole time, just said 'you should just put on about 8kgs...men like a bit of meat on women' - I was 18/19 at the time.
I later ended up taking up to 40 laxatives a day - they now cease to work, so I have to go a bit crazy on natural fibre - god help me when I'm 80 and constipated. Sorry, TMI!
So, yes, fully agree with others - help for anorexia/bulimia is pathetic. I'm sure you do this already, but, please avoid letting your daughter see, feel or sense how outraged you are at the system. She may translates her mother's anger as being directly her fault, and she's going to regress further.
Is it the elephant in the room at your house, or do you talk about it openly? If the latter, have you tried a reasoned approach to things? Nothing pissed me off more than people I barely knew grabbing my upper arm and saying 'omg, look how skinny you are! I need to feed you up' - also, it's a dangerous thing to say because it reaffirmed how "fabulously skinny and in the minority" I was. Instead a reasoned 'why do you do this? What do you hope to gain? Is this really sustainable?' helped me far more. I would also try to diminish it - I know that sounds really inconsiderate on my part. But, treating it as a smaller thing than it is may help her diminish it as a demon in her own head. It evidently rules every waking thought, so you almost have to outwardly live in denial.
Does she have a compromise weight? I hated people fighting with me on my weight. However, some spoke to me about finding a 'still thin', but heavier weight and maintaining that instead. Bit by bit, she may see that, actually, "I was bloody ridiculous before and now I'm happier". If this can be reasoned, I would actively help her e.g. exercise with her, demonstrating that the voices in her head aren't imprisoning her and that she doesn't have to bear the constant exercise-starvation cycle on her own.
I wouldn't take scales away either. For me it was all about numbers. I'm OCD. Lack of scales would make me very anxious so I'd go overboard on starvation and exercise to be on the safe side.
Sorry if you've heard these tips before. If you have, I didn't mean to be patronising.