OP, I think you are getting a hard time here when to me the underlying tone of your post is more fearful than anything else - fear for your daughter and your grand- daughter - I hear denial, and perhaps that you have been watching this situation with a sense of disbelief and growing frustration.
If a dietician “isn’t interested” yet you can see the problem, and you are of a generation that defers to “medical authority” this contributes to confusion too. Also, with so many manifestations of mental distress there is the suspicion of attention seeking and those around the sufferer, when they love them, want it all to just stop and for things to be normal, that they should just be able to “snap out of it”.
Unfortunately, as others have said, eating disorders are usually a sign of needing to feel in control of perhaps one thing in their lives, often triggered by stress and / or trauma. Or perhaps the praise for achieving the socially prized goal of weight loss is filling an unmet need that has been going on for years and without it your daughter may lose newly found self-esteem. There are dozens of reasons that need to be supportively explored, but making her feel bad by saying she’s a bad example to her daughter is not going to help - it will increase feelings of shame and self loathing and perpetuate the problem.
I think you do want to help, so focus on the why to start with, and it will likely take a while.
I was bulimic from 17 to 42 - almost intermittently and my worst periods were during stress and abusive relationships when I felt nothing was in my control. In my 50s now, and have probably what is called disordered eating but no longer purge. I could easily become anorexic but I just shovel in fuel when I remember and try not to think about it otherwise.
I wish you and your daughter strength going forward - use this as an opportunity to solidify your relationship not chip away at it. Fear leads to anger and denial - try to move past that for your daughter’s sake.