The fact that you are 37, with two young children, no priors, and you've put your house up for sale to escape bad neighbours speaks for itself.
I cannot fathom how the police have brought charges of assault against you when no blows were exchanged and therefore your neighbour is sporting no visible injuries.
He has openly admitted to his being at your door with a weapon, so if this gets to court, the evidence will speak for itself. A good solicitor will wipe the floor with your neighbour. Good luck, and let us know the outcome.