both parents need to be on the same page in dealing with this.
Set specific and clear guidelines, with identified results; privleges are retained or removed. Once the guidelines are set, stick to them.
Discussion with the police doesn't necessarily mean an official report will result. Depending on your police force, an officer may be invited to the home to have a little "heart-to-heart" discussion with the teenager, which should include discussions on what will happen to the teenager if the mother even gets a bruise from dropping a plate on her foot!! At the same time, the parents need to support the police in this, and allow the officer to have an honest "attitude adjustment" conversation with their son.
Consistency is key; once they have identified the process they have to stick with it. We had a problem with one of our foster kids and after running through the range of responses, he came home one day and his room was stripped clean......no bed, no dresser, no electronics, nothing. at night he was given a blanket and pillow. gradually he earned the right to have a bed again, then the other privleges. All the kids that come in our house know the rules and whether they are guests, friends, fosters, adopted, biological, the rules are the same. And yes, the rules work both ways, we don't ask the kids to do anything that doesn't apply to us also.
we also had a system with a few other families that we could use. A friend who is a hog farmer loved having "company" for a couple days. Nothing like a few days of working in hog barns, getting up at the grey hours and working harder then they had ever worked before. the kids came back with a new appreciation of life.
this situation can be salvaged, but it will not be easy; they have to stick to it.
if he ever hit the mother again, there should be a good police report attached to his trip to the ER, explaining why he was bounced off a wall, dragged down the steps, and ejected out the front door, with a size 11 boot print on his backside.