it may not be in Tomalin, but it's certainly in Carol Shields and in Deirdre LeFaye that all the Austen children went to the same woman. They seemed to have called her "Movie", and her last name was Littleton, or Littleworth, depending on which book you read. Not only that but Movie had a daughter of her own, called Betsey, and a husband (John?) who worked the farm for Mr Austen. The family were Austen servants still one hundred years later.
Personally, I think Tomalin is way too harsh here. I think the Austens had a permanent nanny in Movie, and perhaps saw the Littleworth family as an extension of their own- trusted family retainers, if you wish. I wonder if, had they lived in larger accomodation, whether the Littletons wouldn't have lived in with them, or at least daily visited the Austen house to look after the children. I guess we'll never know.
At least the kids got their three month's worth of breastfeeding before being fed spooned pap (mushed up bread and milk or water)!