S.T.
First be thankful, so very thankful that your daughter is mentally healthy. Mental health problems occur in families where there are loving parents and good supprt systems too. Also keep in mind that this other girl may not be playing mind games with your daughter intentionally. If she suffers with mental health issues her perceptions are distorted, her reactions will be disporportionate, and her ability to interact with people will be impacted.
As the mother of a teen who suffers from depression I can't even describe how heart-breaking it is. Since my kids were in kindergarten, I've only worked during the hours while my children are in school so I could be home to do homework, be invovled with their activities, friendships, school work, etc. We spend tons of time with our kids, they participate in all kinds of extracurriular activities, they've been raised in a close and loving environment - yet our teenage daughter has been through some very, very deep valleys of mental health issues - including being hospitalized for a short time. She's hurt herself and had a period of time where she made repeated efforts to do so.
I'm saying all of this so you understand that many mental health issues are a result of biological / chemical imbalances. Many of these kids have suffered with this stuff since early childhood - undetected - and when puberty and hormones rage their minds become more and more difficult to balance. This kid is in an even worse situation if her parents are not providing the kind of support she needs. Becuase these kids have been dealing with imbalances since childhood they've never learned how to be a friend, how to react appropriately. The percieve actions as attacks against them, they have a very tough time just ignoring things that bother them. most of these kids don't have a deep circle of friends as a result.
Your daughter has been a kind soul to this hurting girl for a number of years - and your daughter seems to have come to a place in her life where she sees that they are developing separate interests and growing away from eachother. This isn't your thing to handle. And since this girl sounds pretty fragile, a parent telling her to bug-off could be devastating. She will have a tough time hearing that from you.
Instead, allow this friendship to fizzle. This girl will probably be a little clingy since she probably does not have many friends as your daughter probably does. But if your daughter is not available more and more often due to her schedule then it wil fizzle. Eventually the other girl will figure it out. She will probably feel hurt, and may even ask your daughter if she's mad at her or did she do something wrong? Coach your daughter to be kind, help her have answers already prepared - "I just got home from practice and I'm buried with homework", "My aunt asked me to watch my little cousins", "I have to get my chores done or I won't be able to go to my waterpolo game", etc. Youru role here is to coach your daughter in how best to handle this girl - it will help her develop these skills in the years to come.
Be kind in your thoughts towards this girl - she's trying to deal the best she can with an illness that strikes no differently than cancer or diabetes - but is still subject to such stigma and so greatly impacts the person's ability to maitain interpersonal relationships. I pray that her parents will get their heads out of the sand (or somewhere else) and help her the way she needs to be helped.
Good luck with your daughter - sounds like she will do just fine.