"There is absolutely no reason why the approach of Assist cannot be adopted across Scotland and make a difference to all who experience domestic abuse," she said.
"Yes, we do cost but you need to think about the wider cost of domestic abuse in Scotland. It costs the country billions of pounds."
The service is run by Glasgow City Council and is not part of the criminal justice system, but experts say it is crucial in keeping victims safe and helping them bear witness against their attackers.
Dr Mairead Tagg, a Glasgow-based psychologist who specialises in this area, agreed the domestic abuse court system was making a difference.
"I think it's one of the most important, positive, innovative moves in the last 30 years. I just wish there were more of them," she said.
Last year more than 2,000 cases - ranging from vandalism and breach of the peace to more serious assaults - came through court 13 at Glasgow Sheriff Court, which houses the specialist court.
The accused are wide-ranging, including men and women, professionals and the unemployed, people still in their teens to those in their 70s.
Sheriff Raeburn said the court was set up to help victims through the process
Sheriff Raeburn QC, who sits in the domestic abuse court, said cases can be dealt with very quickly.
"All domestic abuse cases are identified at an early stage and they are all dealt with in the domestic abuse court," she said.
"In the event of a plea of not guilty we try to stick to a fairly strict court timetable.
"Our endeavour is to have cases come to trial within a few weeks of the incident, rather than a few months."
Sheriffs who sit in this court are specially trained in domestic abuse, as are the fiscals prosecuting the cases.
Anne Marie Hicks heads the Procurator Fiscal Service's domestic abuse unit.
She said: "Even though the offence someone is appearing in may seem quite minor, very often it's a breach of the peace that are very nasty domestic cases where there can be a huge amount of abusive name calling, really dreadful abusive behaviour that goes on even when there's no violence involved."
In the five and-a-half years since the court was set up, staff said they had noticed a difference.
Ms Hicks said there has been a rise in the number of guilty pleas
Ms Hicks said one of these changes was in the number of pleas they receive from the accused.
"We have had an increased rate of guilty pleas in the court and actually guilty pleas at the very outset, which is a really positive thing," she said.
Defence solicitor Bob McDowall said the court does have some benefits for the accused, but that he has reservations.
"It's quicker, things are fast tracked and it's a better way of dealing with this type of case, because it is a different type of case," he said.
"I do have some problems with it. I think the system can be very rigid, the actual needs or what's appropriate to the individual client I think sometimes is missed."
There is some evidence that the court has had an impact. While some other Scottish courts struggle to reach a 50% conviction rate in these cases, an evaluation of the domestic abuse cases put conviction rates here at 86%.
Hitting Home will be broadcast on BBC One Scotland at 2235 BST on Tuesday 11 May
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