Either they think he is abusing you, but your now trying to cover it up so you can go back to him (which happens an awful lot! Minimising, backtracking, changing stories, reunions after big bust ups including police, it's really common). So you are a liar.
Or they think that you lied about him doing it because you were pissed of at him after arguing, because you really did think it was him or because you have something else dodgy you were trying to cover up (like drug dealers or loan sharks). Then you have wasted their time, police time, dragged an innocent man through the mud and blown up your family, your kids safety and security, for what?
There is no way you come out of this well. There might be a way of him proving himself (if somebody else really did do it and it can be proven) but either way you've lied and risked your child's well-being.
If I was you, I would apologise tell the absolute truth to them. The actual truth. Even if it makes you look bad. Even if it makes him look bad. Even if you're worried it might mean your parenting and judgement and mental health are bought into question. Give them the truth, and then ask them what hoops they want you to jump through. Do every course, make every change.
Honestly I think in this scenario there will probably always be question marks around your relationship, even if he is proven innocent of the window and hitting, there is the rowing and lying. It does seem like a toxic relationship, and so I wouldn't reunite with him as it may have any impact on the outcome of whether my child stays with me or not.