M.P.
This sounds very similar to the way my daughter acted when she came to me as a foster child at the age of 7. I worked full time and so didn't have to deal with it all of the time. She acted differently at school and in day care. One summer she was in therapeutic day care at our local hospital's child center.
CSD did have her evaluated by a psychiatrist who diagnosed her with Post Traumatic Stress Disorder, Oppositional Definace Order and lack of having bonded with any adult. That must have a "fancy name" too but I don't know it. Our counselor had suggested ADHD but the psychiatrist said that her hyperactivity was more likely caused by anxiety. The psychiatrist said that children still have the ability to bond up until the age of 8 or so and offered as encouragement that she slept with a stuffed bunny that I gave her with her This was nearly 25 years ago and medication wasn't used for children.
I went to a Love and Logic workshop, sponsored by CSD, where I listened to Jim Fay describe a residential program for children who had failed to bond with their caretakers. This facility had a rigid schedule for every day of the week that required children to have chores and natural consequences for misbehavior. Parents can't do this at home but he suggested that children who chronically misbehave will benefit from a definite routine, realistic expectations of good behavior, and consistent natural consequence for misbehavior as well as lots of acknowledgment for good behavior in the form of praise or extra time with the caretaker.
Jim Fay alone with Foster Cline have written several books on love and logic parenting. I strongly urge you to read Parenting with Love and Logic. I think this was their first book. They may have another book that will fit your situation better. They also have a web site.
Unfortunately, I'm not a routine sort of person and I was unable to initiate much of what they suggested. But, what I did use, helped. I've finally been able to adapt my responses to misbehavior more consistently as a grandmother and I find that it does work.
The one natural consequence that I've found that helps me best is the natural consequence of sending the child to their room when they misbehave. The logic behind it is that they are disturbing you and you do not want them in your presence until they are able to behave appropriately.
I could not use this with my daughter because her separation anxiety level was too high. But when she pulled a knife on me, I immediately called a friend to come over and stay with her. I also immediately put all knifes and scissors out of her reach. I kept them hidden except for a couple which I kept in the back of a top shelve when I wasn't using them. This sounds extreme but it's necessary to ensure everyone's safety. It is a natural consequence.
As to her choking her little sister. Never leave her alone with her sister! Never!
The unsafe behavior is caused by anger. Her "shrink" should be working with her on appropriate ways of expressing anger and should be helping you learn ways to help her learn. If he isn't ask him about it and ask for help dealing with her anger.
A very good book that has helped me is How to Talk So Kids Will Listen & How to Listen so Kids Will Talk by Adele Faber and Elaine Mazlish. They use many actual examples of conversation. The book is short and an easy read. I was surprised at how a seemingly minor change in the way I worded by comments changed my child's response. She did fight back, which is called "change back" reaction for a couple of months as both of us got used to the new way of talking but once I was able to be more skillful and she realized I wasn't going to change back, it helped tremendously.
What is important is to acknowledge her anger. It's OK to be angry. It's not OK to hurt anyone. Then give her ways to deal with her anger. For my grandchildren, I started having them run to the end of the hall or do jumping jacks when they were preschoolers. Every once in awhile my 10 yo granddaughter gets into a mood and we go to the playground for an hour or so. Running still helps my grandson who is an immature 7.
You have so much more help than I've ever had or my daughter, both of whose children have been diagnosed with ADHD and her son with ODD and now possibly autism have had. Perhaps you need some help in finding a different way of utilizing the help that you already have. Are you asking them for suggestions of ways that you can change what you do that will enable your daughter to change her behavior. Are you using their suggestions?
It could be that your daughter needs residential treatment. Have you asked about that. If you're hesitant about doing this, spend more time learning about the ways it will help her and you. Sometimes, temporary separation is the only way that will change a child's behavior.
What has her "shrink" actually told you that is causing him to not rule out anything else? First, what are his/her credentials and how experienced are they in dealing with this sort of behavior? Is this person an actual psychiatrist? If not I recommend that you take her to a psychiatrist.
Is it possible that you are not understanding what the "shrink" and the in home therapists are telling you. Could you try finding a way to reduce your anxiety so that you can listen better. Do you take notes? Do you follow their advice/instructions? If you feel that they are not taking action quickly enough, realize that finding the best way to help a child takes time. There is no quick way to do this. I've been frustrated with how slowly evaluation and treatment went.
I suggest, if you haven't already, that you take her to a developmental pediatrician. My daughter should have done that years ago with her 7 yo son. We didn't know about this field until recently. My daughter was relying on the school district for evaluation and treatment. Because their treatment was not helping my grandson reduce his angry acting out at school his team recommended seeing the developmental pediatrician who added a tentative diagnosis of being on the autism spectrum disorder span. He's also, as a result of this visit, now taking medication for ADHD and is calmer in just 2 weeks.
Hang in there and keep asking for help. Eventually everyone will get it figured out. I do urge you to put away sharp objects and never let your older daughter be alone with your younger daughter. I also urge you to find ways to spend time just for you. You are drained and need a massive refill.