You don't have the full picture Op.
Why does she have an injunction against him? He must have done something really bad for an injunction to have been awarded. Not in her opinion, but in the opinion of the courts.
Or he is lying to you about the injunction and it doesn't really exist.
Either way, you don't have the full story.
She can't stop him seeing his children - unless a court has said so (and again that would be only if he'd done something terrible - they rarely stop children seeing a parent). So again, either he has done something dreadful, or he is lying to you about her stopping him.
Aside from all of the above, why is he not stepping in to stop this madness? Why is he saying YOU have to talk to the police? Why is he not concerned that your / his child is receiving death threats? Does he not see that as his job to deal with? Especially when it's HIS ex making the threats. Why doesn't he instinctively jump in to protect you? At best he is wet, weak and doesn't care much.
I think you are being lied to. Your partner certainly doesn't have your back. And that is why he gets angry when you express concern about all of this... because he is trying to cover up a story and he doesn't want you to get close to it.
Think about it - he has family members who are in close contact with her. Why would they do that if she was so awful and he was the victim in their relationship? Could it be that those family members saw the relationship play out and think he's treated her and their children badly?