Ok buddy - I'm gonna try to twist your head around here, so get ready.
And believe me, I know whereof I speak - my daughter had anorexia and bulimia when she was 12 and 13, and this last year in college had a serious depressive episode requiring an outpatient psych program.
I'm also an M.D. and believe me, I learned everything you never wanted to know about this stuff when my kid got sick.
So here goes:
1) YOUR DAUGHTER IS SICK WITH A LIFE THREATENING ILLNESS. It's as if she has leukemia or lung cancer. Your ex wife did not cause this to happen. Your daughter did not cause this to happen. There is good evidence that damage to the basal ganglia in the brain, likely from antibodies, is involved in eating disorders and OCD. She has a monkey on her back that is causing intrusive thoughts and you need to partner up WITH her against those intrusive thoughts, rather than blame her for her eating disorder. Some cases, for instance, are caused by strep antibodies - would you feel as angry at your daughter if you knew THAT was the cause? You will need to learn to be angry at the DISEASE, not at HER.
2) Please read a brand new book called Brain on Fire by Cahalan. It's not about eating disorders per se - it's the story of a young journalist who became psychotic due to antibodies against NMDA receptors in her brain. But this is probably just the tip of the iceberg when it comes to autoimmune diseases causing brain disorders. It's a quick read and I think will help you change your perspective.
3) You need to share this stuff with your wife. Your ex did NOT cause the eating disorder, (despite all the1980's psychobabble explanations of eating disorders which are a LOAD of BS), and your current wife is NOT being expected to clean up somebody else's mess. Your current wife is being expected to help support you while you support your daughter who has a life-threatening illness.
4) If you can afford it, start with an inpatient eating disorders program. If not, I have some ideas for you. I'll write more later when I have more time, and I'll get you some more resources. But you have to stop blaming the ex, and stop blaming your daughter, and just deal with this illness. Believe me, I know how unfair it feels.