In the Dursley family, who were the very picture of contentment, there was just one secret.
My translation of そんな絵に描いたように満ち足りた is purely a guess based on Jisho's definition of 絵に描いたように as "The very picture of...".
I can't understand how this phrase is used. Literally, I would translate そんな絵に描いたように満ち足りた as "Contented as though they had painted on such a picture". So I can kind of see how it works, but what is そんな needed for?
Could you give some other examples using this phrase so I can get a better feel for how it works?