I think the first thing to do is start ABC (antecedent, behaviour, consequence) charts to try and see if there is a pattern to the behaviour. It's good the teacher recognises it's "communication issues" but you would all definitely benefit from analysing that a bit more.
I bet that after a couple of weeks you'll see that there are triggers and a pattern to it. It might be attention-seeking (ie she plays up and gets more attention for it), might be avoiding the work if it's too much for her, it might be sensory problems (overwhelmed by large groups). If it is as the teacher says, when the work gets too much, that's a clear indication that she needs more tuition and support with this, eg prep in advance on what topics are coming up. My ds really plays up (not aggressively but just gets really silly and tries to get a laugh) when the work is hard for him. It's a smart way of getting out of the work! If she has SLI keeping up with topics being discussed at carpet time will be really hard for her, so it's not surprising she's playing up as she probably isn't understanidng half of what's going on.
Anyway. Once you have some clear data on when and why it is happening it will definitely help with formulating a plan of what to do, how to avoid it.
But in the meantime, I would be pushing for an absolutely zero-tolerance approach to this. It sounds like, as zzzz says, she is getting more attention for aggression, which is totally reinforcing the behaviour. So she needs to get the idea that hurting others results in no attention, no special treatment for her, and actually something negative happening. Depends whether you do "punishment" or not but this could mean withdrawal or removal of previously-promised treat (like the tennis ball thing), or a simple time-out (more grown-up equivalent of naughty step) where she is immediately removed from the situation, put on her own with no toys or distractions. She gets no attention, except telling her once "dd you are going in time-out for hitting".
Could also try tick/cross charts, we do these with ds sometimes. At the beginning of the day he gets a blank chart with 10 spaces for ticks, and 10 fr crosses. Each 'good' behaviour gets a tick, each bad gets a cross. It is amazing how much more he is motivted to get ticks than he cares about getting crosses.
The bottom line is that she should get tons and tons of attention and praise lavished on her for behaving nicely without being aggressive, but no attention (except for removal) when she is being aggressive.
(This is our ABA approach btw - I've tried to simplify it for everyday use!)