What happens if you contempt Court by breaking a contact order for an abusive father to see 2 year old girl?

You answered your own question.... you could go to prison I'm assuming a court has already granted him access? because it is a sensitive matter I would suggest you seek legal advise as a mum myself I can understand why you would want him to have no access at all but you need to go through the proper channels to do this as your little girl needs you at home not locked up