Anybody can ask anything.
However, they will not tell you. It is subject to data protection regulations and other they would not want reprisals as that creates a public order problem.
You are perfectly entitled to attend court and hear the evidence. If your daughter doesn't co-operate then you can always report her to social services as that is just plain failing to protect her child.
Good to see you are focusing upon the right person. If your daughter chooses to live with a violent man that is her free choice. A child is a different matter entirely.
Do not let her make you responsible for her poor choices though.
Can I clarify anything for you?
Claire's law won't really help all that much. It will only tell you whether he has any history. Since you know there was an attack anyway that really doesn't add much.
The police will make a report if they feel there are child care issues although the absence of a charge might indicate there are doubts over her evidence.
If I were you though I would report it.