I'm so sorry for your situation- you must be so worried.
I went to court with representation and what I learnt from watching my v experienced solicitor is actually not to say too much at all.
In the first hearing you just want to get the court to order a "wishes and feelings report" so that the child's views can be taken into account. Keep acknowledging the right of the child to enjoy good relationships with both parents and keep saying you just want the court to hear the child's wishes and feelings.
Don't make accusations etc just get that report ordered.
CAFCASS will then talk to all of you, my dd was 11 and her views were given considerable weight. Don't slag off your husband, keep reiterating how pleased you are that he cares about his dd and how important it is that they have a good relationship but that you're concerned about the DV. Explain that dd is growing up in a situation that is causing her stress and may lead to lifelong issues which could be avoided. I know it's hard but be moderate and calm. Avoid getting drawn into circular arguments you can't win. They will try to paint you as neurotic and vindictive. Don't give them any ammunition.
If your dd wants a different contact arrangement she needs to tell CAFCASS. My 11 year old dd was listened to seriously.
If it goes back for a further hearing: stay calm, present the CAFCASS report and just keep reiterating that 11 yo dd has a right to be heard and to have her views taken into consideration. The court is only interested in her rights not your's or dad's.
Good luck. My solicitor said very little. It was a good tactic.