I often think that ADD/ADHD are really ways of expressing a neurology similar to autism. I wonder if younger daughter is struggling with a lot of the routine/rigidity/communication issues that get focus in her older sister, and isn't really able to tell you what she needs.
Of course, this kind of situation is hard on any sibling of any neurology: it must be frightening to know that your sister might have died, and I can completely see that one way to handle that fear is to minimize it (meaning turning "might have died" in your head into "being an attention hog.") That would explain a lot of the behavior directed at her sister.
Can you get your second daughter her own social worker/counselor? Sounds like at the very least, she needs somebody's undivided attention to process everything that's going on, including her own neurology. Since she wants you to buy her things, tell her in advance that you will buy her X (you make the call, otherwise she will keep upping the ante) if she makes an honest effort with a counselor.