I recall a scene in a book which i thought was Penrod, by Booth
Tarkington, but on re-reading the book couldn't find that passage.   The story,
set around the early 1900's, involved a young boy who'd brought a
stray dog home.  He'd hidden it in the barn, or some outbuilding,
because Mother wouldn't approve.  In order to feed the dog, he took the
(lamb)chop his mother served for dinner and put it in his shirt.  His
mother turned around and asked what happened to the chop.  "I ate it,"
he said.  "Bone and all?"  "I was hungry".  And then comes the line
that stuck in my mind, which goes something like "And then, in the
manner of grownups, she let this tantalizing mystery go unsolved, 
something no self respecting child would ever do."

Does ANYONE know the book this came from?

Hi there..... could this be
OLD YELLER
It sounds real similiar, story of a dog, and a kid, set around turn of century.
Maybe that's it?

no, unfortunately, that's not it.  totally different social context. 
the family i recall was one of those (post?) victorian, more
urban--even tho there was a barn it was more like a carriage
house/garage. (don't recall if they had a car... that line about
unsolved mysteries is the ONLY thing i remember about the book).