"I dont know how to prove it wont happen again"
You cant. But I fear you will have them on your case for as long as they think you are standing by your man, rather than your children.
If you look at your history together, with drunken violence, reported 3 times, (How many times did he trash the place, or throw plates, smash doors and windows that was not reported to the police?)
In addition to a violent nature, he developed a mental health problem so severe he was hospitalized, and this coincided with you falling pregnant with your second child. This child is just a baby. I can see where they are coming from. You seem adamant he has changed. But you have no proof, and neither have ss, they can only go by the past. And your past together is not rosy. They are your childrens advocates, and they cant risk another baby death. I am sorry, but are you reading the news? A child die by their parents hand monthly, and every time the ss is scrutinized for fault, and criticized for not having picked up on risk and acted on it.
You sound eloquent and thoughtful. I think you need to separate yourself from your situation and try look at if from SS perspective, and as if you did not know the people involved.
Instead of looking at the obstacles you perceive that SS are laying in your course, try look for ways to jump through the hoops and work with them to safeguard your children.
Are you scared of him? I think you are. I think you are scared of the repercussions of being seen to side with SS, and not him.
I think you are scared that he will "loose it" if you work with them rather than him, and that you are "managing" his temper and his mental health by placating him. As long as you both appear to just do what ss tells you to without putting up too much of a fight, he can still have the impression that you are siding with him, as your ultimate goal in his eyes MUST be that you do this so that he and you can stay together and you keep protecting him and being HIS advocate, rather than your childrens.
I may have it totally wrong, but that is what is jumping out at me, judging by what you say.