I think that very often the biggest barrier to a successful outcome (see below) is the victim herself (I’ll use “she” and “her” because of this particular example, but I realise that DV victims are not necessarily female).
It is common knowledge (I think) that DV victims suffer a large number of assaults before contacting the police. Last time I looked the average number was around twelve. But on top of this, police and CPS files are littered with failed DV prosecutions. This is because of, what I call, the “he loves me really” syndrome. A victim gets beaten, contacts the police who arrive, arrest the alleged assailant, take a statement from the victim (almost always the only witness) and off the matter goes into the judicial system. At some point between then and trial day, the victim decides she only called the police to frighten him, wants no further action taken, does not want to see her man in trouble because “he loves me really.” The CPS has a policy of prosecuting DV matters even without the victim’s support whenever possible, but it is a big ask. I have seen victims served with a witness summons (something the CPS does very reluctantly), turn up in court to find that their memory of the events (which led to them receiving various injuries, the signs of which are often verified by a police doctor) have faded. They “cannot remember” having seven bells knocked out of them, or who did it and how.
The only satisfactory outcome for a DV victim is complete physical separation between the victim and her assailant. Nothing else works. DV perpetrators do not “get better”. They get worse. Your friend, together with her child, needs to get away from the partnership immediately or sooner. She needs to support any prosecution the police and CPS instigate. She needs to attend court and give evidence if necessary and ask the prosecutor to request that the court makes a restraining order (which can be issued with or without a conviction).
I know I have made this sound simple but I fully appreciate it is anything but, especially when there is a child involved. But it’s the only way.