It is important for you to discipline your daughter when she acts aggressively. I understand your hesitation, but it is not helping her to refrain from discipline. Otherwise, you are unwittingly condoning, or at least reinforcing, what she is doing. Now, limit-setting may not be all you can do. It would be prudent to arrange an evaluation with a child psychiatrist, who can then collaborate with your daughter's other health care providers in order to reach some conclusion about possible pharmacological treatment to diminish her impulsivity and aggression.
My son was like that when he was younger. We went to see a pediatric neurologist who recommended an occupational therapist and a speech and language pathologist, as well as giving us some tips on behavior management. I have to tell you that the kicking and biting did not go away immediately. As you can imagine, a child with all those difficulties is already very angry and frustrated. We added a child psychologist after the other services had been in place for a short while. What seemed to register with my son was that people were trying to help him get better, and that seemed calming. The other thing that my son had, and this may not apply in your situation, was an allergic reaction to milk and dairy. He had a terrible history of ear infections in particular, and was constantly on antibiotics. When we removed all milk and dairy for three months, there was a change in not only his health, but in behavior to some degree as well. The pediatrician attributed the behavioral change to his just not having the additonal physical pain to deal with. Hope this helps. Good luck to you.
My kids are preschool age and similar to your daughter inasmuch as they seek out a lot of intense sensory stimulation. To reduce the biting I try to just avoid situations I think might cause them frustration. This obviously is not always possible, and I'm sure you are laughing at me right now!
But the other thing I found really helpful with the mouthing (not the agression part)is to provide lots of really challenging snacks to give their mouths heavy work. Hard beer pretzels, Stella Doro breakfast treats, fruit roll ups, swedish fish, Laffy Taffy. Heavy duty chew food. Just make sure she's mature enough not to choke.
I even bought a vibrator, on the advice of our OT, for them to put in their mouths. Embarassing when guests visit? Sure. But they really enjoy it.
Do you think that your daughter has sensory issues? Does she like to eat because it is filling a sensory need? You could try reading the book, The Out-of-Sync child by Carol Krandowsky(?). It really tells a lot about children who are aggressive because they are seeking sensory input, want to touch, or be touched and since they are not having that need fulfilled to the extent to which they want, they become very upset. It is not a very expensive book, only about $15.00. It certainly opened up my eyes and made me look at this problem differently.