There is no doubt you don't want your younger children following suit with your oldest daughter's behaviors. Anxiety certainly can play a part in a person's behavior, but it does not give her the right to mistreat others. You mentioned you have been trying to get her help for the anxiety for a number of years. We don't know what all you have tried, but if nothing has worked and nothing has ever changed, you may need to go back to square one and even start with a full mental health evaluation.
If she is struggling with anxiety and everyone else has been trying to control it, sometimes that backfires. An anxious person may even feel more trapped. Think about what she does to manage her own anxiety. Try giving her the tools to help calm herself. This might include daily medication, yoga, working with a therapist, exercises, or a list of coping skills by her bed.
At the times she becomes violent or talks back, remind her of what she can do to bring herself to a calm, but do not get drawn into an argument with her. Once things have calmed, re-engage. She needs to know what exact behavior was unacceptable, what the correct behavior should be for the next time, and what her consequence is for her behaviors. You also can make her privileges available only if she participates in services to learn to manage her anxiety in acceptable ways. Some of her behaviors may just be habits she has gotten into over the years. You mentioned she went to a behavioral health center. If she is not currently working with a behavioral therapist, that may be in order as well.
As for longer residential placement, other than psychiatric facilities, most will have an admissions process that looks at her behavioral, mental health, educational, and medical histories to determine if she qualifies for placement and if they can meet her needs. In order to qualify for many long term residential facilities, other less intense treatments may be required first, to make sure you have tried all of the less intense services.
If you are interested in looking at the Boys Town Family Treatment Homes, please take a look at boystownadmissions.org. There is a plethora of information on the program.
A Boys Town website you might want to take a look at is yourlifeyourvoice.org. It is actually a site for teens, but there are many different articles on anxiety, coping strategies, and relationships that you might find helpful, and may even want to print off for her.
