I think June had real issues herself and Colin Caffel (the twins father) goes into a bit more detail in the book he wrote.
Neville though was described as warm and friendly.
Jeremy has issues with the fact he was sent to boarding school aged 7. He resented his parents for this although in their eyes they probably felt like they were providing a wonderful education for him.
Sheila was very frail emotionally and I'm not sure when June's mental health deteriorated so badly but certainly by the time the murders happened she was asking the twins to kneel and pray at bedtime which they didn't like. Colin Caffel definitely spike to her about this. He also says that visits to her parents always damaged her emotionally but that at the time she'd just come out of hospital and was n a good place. He doesn't believe there is a chance in hell she would murder her children.
I believe Jeremy is guilty but would also never be surprised if he was eventually released.
The one thing that does surprise me is the change to a whole life tariff. We've seen other people guilty of several murders released after long sentences. It makes me wonder why Jeremy had his sentence increased. It does suggest that the authorities have real concerns about him back in society perhaps.