The child being removed is not about blaming or punishing the mother, it's simply about protecting the child. If the op hasn't been reporting him to the police and the child is in danger than as a minimum this is a prudent act.
Let's not forget the child has already been hospitalised by her father, that he comes round threatening to kill them and smash the place up. Whatever we hear here, a judge and social services felt it was in the child's best interests to remove her at this stage for her own protection.
The op needs to work with social services, " an improvement" is clearly not enough and she will need to comply with whatever they need done to ensure the child's safety. I suspect she was doing what she thought was best out of fear , but sometimes when we are scared we don't act rationally. The child was still witnessing or hearing the threats and the mother was having to get her out her own home.
That's awful for any child, never mind the mother.
Ps, please stop the troll huntng, I don't think it helps any, I'm sorry. The mods have reviewed, let's trust their judgement, we all act differently in times of stress.