@Tyr that's horrendous. Please take care of yourself - it sounds really traumatic. I'm glad you've found the forum - I have found people here are compassionate and supportive. I will tag you in the 'introduce yourself here' thread. To see when someone tags you, replies, supports one of your posts, or posts in a thread that you've been active in, check the little bell in the top right of the screen. To tag someone use @ then their forum name.
Try not to hide away - you did nothing wrong and need support. In fact, it sounds like you and your family have been the victims of crime. My son and I found ourselves in that position (not at hands of police) and I was surprised to find out that there is a victims of crime government agency that can help. They did not push us to press charges though that was an option. They offered practical support and counselling, and there were no fees. It was a great relief to find them.
I do not have a lot of faith in the police to investigate their own. Write down as much detail as you can remember, including witnesses if you're able to identify them. Then if you choose to seek legal advice do so as soon as you can - there are legal aid offices in each state/territory https://www.australia.gov.au/content/legal-aid
Also, there are lots of no win no pay outfits that take a slice of your compensation, but you don't have anything to pay up front. Ask about wrongful arrest, assault, harm to reputation and damages.
Re DoCs or whatever that agency is called - I doubt they are obliged to investigage where there are no grounds. What they told you sounds more like it would be more work for them to fix their mistake than to just go through the motions. They will have a complaints section. If you chose to go down that path, make some notes as to what you want to happen.
I'm sorry that this happened to you and yours, and I'm thinking of you all.
