While this answer doesn't address whether or not the story was a hoax, per se, it does summarize the commentary from this review of Dr. Ian Stevenson's book which discussed the case.
First of all, Stevenson did not witness any of the sister's behavior himself.
The 14 cases he cites [in the book, including the Pollock one,] rely on nothing more than anecdotes: all the “past life behavior” had been witnessed before the author met any of the players and so the veracity of the stories is hard to determine.
[T]he author had got involved in none of these cases until some considerable time after the children were reported as remembering their prior lives. Thus they were all just anecdotes, although well documented and cross referenced.
The reviewer then notes that this story falls into the category of examples where the reincarnated person's identity was known, but the family of the deceased had contact with the "reincarnated" children. (Or, as in this case, was the same family.)
He then describes this case as follows:
Two twin girls (aged six and eleven) are tragically killed. The father was a strong believer in reincarnation, and was sure they would be reborn to his wife as twins. Twins are born, and between the ages of 2 and 4 they start making statements about their dead siblings.
As the father believed the twins were reincarnations of their dead sisters, it is likely that he talked about it in front of the baby girls. It’s also likely that friends and family talked about the tragic death of the previous two girls. It’s hardly surprising that the girls are reported to have talked about their “previous lives”. The parents could also be reading too much into the twins’ statements, or could be lying. We’ll never know.
It's often said among skeptics (and scientists in general) that "Extraordinary claims require extraordinary evidence". In this case, the evidence is really quite weak.
For the park example, for instance, it would have been trivial for the mother to have taken the children to a park with a friend, and to have said to the friend's parent something along the lines of "I don't like this park as much as the one that Jacqueline used to play in". One of the children, overhearing that, could then have asked to go to "the other park". Since the mother was primed to believe in the daughters' reincarnation, she'd then interpret that as "It's a park they'd never been to before!" rather than simply assuming the child heard of it from someone. Five years later, when she's retelling the story to Stevenson, she no longer remembers her off-hand comment to her friend, and only remembers the request.
Whether that's an accurate scenario, there's no way to say. But it's a plausible one, which is enough to require further proof of the extraordinary claims being made.