We stay in first floor. When ever my 4 and 6 yr kids run/jump around, the neighbor on top floor complains of too much noise. They misbehaved by kicking the main-door and showing there anger on the kids and my wife when I was not at home. We complained to manager but nothing has happened. They make noise in the middle of night but we are not able to prove that. I tried explaining them but no use. What should I do in this of situations.

Be a good neighbor and stay on your manager's case until you are satisfied. Other than that, look for a new home.