Well, it seems pretty unlikely she will get what she wants based on what you've described. It's going to hinge largely on what the family report says though. Yes, the family report writer should (should! not necessarily will) be aware of the timeframes and provide the report in advance of the hearing - usually at least a week or two beforehand to give both parties time to provide submissions with updated proposals based on the recommendations of the report. At least, that's how it worked in my case.
Family reports tend to be reasonably conservative, not rocking the boat in terms of existing arrangements unless there's a significant issue identified. Most likely, the report will recommend progression of the mother's time over a period of months/years, possibly with the view to 50/50 eventually, but probably not a reversal of the primary care as she wants.
You've had time to establish yourself as the primary carer and there may be still be doubts about the mother's violence. These are just my own gut feelings, I'm not a lawyer and I don't have any particular insight into what the report will contain, I'm just someone who's had two family reports done and know roughly what progression is likely.
As for the hearing, Sammy may be right about an adjournment. But I think it's possible that the family report will be released in time. I had similar timeframes and it came through at the last minute. I don't know whether changes to arrangements could be made at a directions hearing, which is usually just to provide 'direction' for a future contested hearing. I suppose they could if it was by consent?
