I think the problem is with the nursery rather than the aggresive child. Surely the pre school has ratios of 1 to 3 like other nurseries in this age group. Prehaps the little girl's mum should be asked to stay to help if one to one funding is not available. However it does sound as if the family desperately needs respite.
No two year old child should be kicked out of nursery. Instead there needs to be suitable involvement with outside agencies. I think the aggressive child needs to see a community paediatrian to assess development. Prehaps the community paed can refer the child to SALT, audiology or a pychologist.
I also wonder if the aggressive child has witnessed some violent behaviour or has been abused. Children aren't born evil.
No one likes their child being attacked, but I feel the parents of the attacked child have lost all sense of proportion. Going to the police about the behaviour of a two year old is plain daft and referring to a toddler as "Chuckie" is a form of bullying.