The argument with the 37-year-old started near a white van parked on Bouley Bay Common at about 4 pm on Friday.
The younger woman was later arrested on suspicion of grave and criminal assault but has since been released on bail. The 71-year-old is now out of hospital.
Police want to hear from anyone who saw what happened near a UK-registered Renault van that had black dog stickers on the back of it.
Witnesses should call Police Headquarters on 612612 or Crimestoppers anonymously on 0800 555 111.
