I wish I could offer a solution, but the reality is that even with extensive professional help hoarding does not have a high success rate in terms of bringing it under control.
And it is a godawful environment, physically and mentally, to have to live in as a voiceless, powerless child in the equation.
I am 50 years old. Long free of my mother's hoard (even the one she shipped overseas to my house a decade and a half ago) and I still suffer from doorbell dread.
An unexpected guest sets off something close to the beginnings of a panic attack, even though my home is (mostly) clean and tidy. I have no reason for the state of my home to set off the Tsunami of shame that comes with their arrival. But it smashes into me anyway.
If we have expected guests I end up in a three day emotionally distraught state of making the house perfect. Washing it as some kind of hysterical displacement activity, cos I am mostly trying to mentally wash the stain of squalor and extreme disorder off me. The hoard has gone, but in some ways I am still living in its ghost.
Don't under estimate what his mental health issue can mean for your children.
Becuase it is all too easy for the non hoarder to get worn down and stop seeing the hoard (it can kind of get normalised in your head to being not as bad as it actually is) it might be worth considering getting a warm, but honest outside opinion. A mate, a family member, somebody you trust to not reflect back at you what they think you want them to see.
If you can't do that there are some helpful illustrated guides to help you work out the scale of the issue as it stands today. (I'll add the links after).
Once that is done you can monitor and log the state of the hoard. Which is essential, cos a lot of post "almighty great row and threats of leaving" movement looks like it is going in the right direction. However with objective evidence it can be clearly seen for what it is. Just more churning, with nothing going out and no order being created. Merely a shifting of the composition and placement.