I don't recall reading anything about June suffering a breakdown close to the murders. I would have thought that if her health had given so much cause for concern that either the housekeeper or Barbara Willson would have noticed it and mentioned it, however I will allow that as she was probably highly strung she may have been on something to reduce anxiety. I wonder where on earth an author, long after the event, would get such information.
Because of June's health having been delicate,Neville was caught up in where his allegiance lay,as he'd always supported Sheila,but this time,it had been concern for June and I don't doubt that wouldn't have gone down well with Sheila. After Sheila's stay in hospital in 1983,she went to WHF to recuperate and June had given her short shrift by saying that she wasn't the only one who'd been unwell,or words to that effect. In other words,as Sheila told her friends that her mother had offered no sympathy.
BW possibly did know,but she's not likely to have said anything being a family confidante. Even less likely now since her latest video.