You don't give a whole lot of information about the behavioral problem is but I would think that it could possibly be caused by your daughter's auditory processing disorder. She may feel frustrated by not being able to hear everything and process it as quickly as maybe others expect that she should (teachers, her friends and classmates, family members, her own expectations of herself).
Even though she doesn't act out at school, it could be possible that she could be bottling up her frustration during the day and letting it out in her own safe environment: home. I'm not saying this is the case but just a possibility.
What I would do, if I were you, is start keeping an ABC chart ("A" - antecedent, "B" - behavior, "C" - consequence). Whenever you see a behavior at home, note down the day and the time, what was happening before the behavior (eg., "Little Sister asked Ann to play playdough with her three times and when Ann didn't respond, Little Sister hit her"), what the behavior consisted of (e.g., "Ann screamed at Little Sister and pushed her"), and what was the consequence, (e.g., "Ann got time out for 8-minutes"). If you track this information over the course of a couple of weeks and take a look back at it, I'm pretty sure that you will see some commonalities in the events and some red flags. This will help you better understand if there is a CAPD issue that needs to be addressed, a family dynamics issue, maybe an environmental issue (e.g., sensory overload from too much noise), or possibly a social/relationship issue that she hasn't been able to articulate to you (e.g., problem with a friend).
I would also suggest to you that, if you are not currently working with a speech therapist at this time, then maybe this would be a good time to have her re-evalauted to determine if further treatment is necessary (that's who we worked with for my son's auditory processing disorder). Or possibly a child psychologist or developmental pediatrician assessment would shed some light into what is going on.
I hope that you are able to get a handle on this soon. I know it is not easy for you when she has her behavior problems and it must not be that easy for her as well.
Best wishes.