Hi D.,
I can imagine this is a real pull for you. Here are my thoughts.
Your friend is really struggling and probably does not know what to do with her child, and she most likely was hanging like crazy to the fact she had a "friend" in your daughter. Having said that, you have to advocate for your child until she is old enough to do it for herself. It would be best to tell her that you feel so badly, but you really want to see your child develop some friends that may be better suited to get along with her. Try not to criticize, but say, "It is just really hard for <mandy> to figure out how to work around your daughter, being so assertive, and we think it will be good to give her a chance to develop other friendships, so that later, she can maybe be better at knowing how to be friends in yours".
Maybe she will open up, it may not be all your friends fault that her daughter is out of control. Many times, kids that have these type issues are exaserbating and the parents learn none of their skillsets work anyway. If she gives you any opening - which she must extend, do not reach in unless she is ready - recommend that perhaps this book would be helpful:
1) Healing the childhood epidemics by Kenneth Bock (she will have to read it before judging because she will not want to accept that her daughter is having these problems)
2) Scream free parenting - setting boundries and consequences that can be followed through.
Having a child with these types of extreme behaviors is so painful, because like you, the parents believe it is all their fault, yet nothing they do works. Your friend needs your support and love, all the while you are drawing boundries for your child and what is good for her. It is a tough line, but while you may be convinced that she and her husband are terrible parents, you have not lived and failed with that child. It may be painful for you, but it is gut wrenching for her, because she knows what she has and she is scared of the doom that lays for that child.
Hope that helps, J.