The sentence in question: しかし、不思議なことに、そう答える親たち自身の幼い時の記憶には、自分がおんぶされていた頃の思い出が強く残っているのです。
My attempt at translation: "However, about the strange thing, the parents who answered that way, in their memories of the time where they personally were young, there are strong memories left where they were carried on the back themselves."
I wonder how 自身 and 親 are related. The way I parsed this sentence is
...そう答える親たち | 自身の幼い時の記憶には...
The parents who answered that way
concerning the memories of the times where they personally were young...
I wondered wether one could put a の between 親たち and 自身 but I couldn't come up with a meaningful translation for that one. Splitting the sentence into two parts worked quite well for my translation, but I have no idea wether this reflects the actual japanese construction.