The only person who has ever mentioned the twins being put into care is Jeremy bamber. June & Nevill couldn't have done it even if they had wanted to as it wasn't their call to make, especially as they were living with their father at the time.
With respect, I disagree. Sheila was greatly dependent on her parents' financial support.
June and Nevill bought and owned the luxury flat in London where Sheila lived with the twins. Sheila was on benefits and rarely worked, she could never have afforded this flat had her parents not financed it.
Sheila's lifestyle with her friends, who Powell calls the 'Gorgeous Girls', the clothes Sheila wore to the weekly glamour parties with lines of coke on the table that Powell states Sheila's friends told her Sheila attended - all of this was subsidised by support from Nevill and June.
This, in my opinion, suggests that June and Nevill would have had considerable influence over Sheila's and the twins lives.