I may at some point do a list of recommendations, for anyone who's interested, but I did want to mention one in particular: Peepo! by Janet & Allan Ahlberg. Uniquely among the Very Young Children's Books I've encountered recently, it has an entire layer to the narrative which wouldn't be fully apparent to any reader except an adult, and which I've found haunting me oddly over the past few weeks.
Peepo! is on the face of it a charming, only slightly twee narrative in verse about a baby's day and what he sees -- his family and their surroundings, mostly -- at various points during it. There's occasional adult commentary as part of this ("And a dog in the doorway / Who shouldn't be there"), and it's assumed that the baby can identify his parents, sisters and grandmother, but for the most part his viewpoint is presented -- realistically enough -- as a collection of unrelated visual experiences. He wakes up, watches his family perform various domestic tasks, is taken to the park, given a bath and put to bed. On the surface, there's no more to it than that.
The adult reader will presumably spot at least that the illustrations and a few of the words ("And his father in the doorway / With a bucketful of coal") put the story in a period context, that of a working-class family sometime in the early twentieth century. Only a fairly close examination, though, will reveal that this is specifically the early 1940s, and the sergeant's jacket hanging over a bedroom chair in the second illustration. The trip to the park in the afternoon is with the sisters and grandma, and the group return to find the mother asleep and the father, who began the day in civvies, wearing khaki shirt and trousers.
Having said his (presumably passionate) goodbye to his wife, the father bathes his son, kisses him goodnight and -- again presumably -- leaves his family to go and fight. The baby, of course, has no more idea of this than the book's infant readers, although the final question of the text ("Fast asleep and dreaming / What did he see?") might invite us to consider his future.
For an adult reader who spots this hidden story, the book becomes a very different experience from that which any child -- even one a fair bit older than our R.'s nearly six months -- is likely to get out of it.
Which is what you need, really, when reading the same twelve cardboard pages over and over again and optimistically aspiring not to lose your mind.
 I say "wife", that being the default assumption of the era, but in fact the mother's hands are clearly visible in several of the illustrations and this is the only one where she appears to be wearing a ring. In this interview Allan Ahlberg mentions his own experience of illegitimacy in the '40s, adding -- probably redundantly, in fact -- that "I was the Peepo! baby".