I found this out by going to the library solo with my daughter. When we can, the three of us go together. That way, my husband reads to D while I pick out really good books to take home with us (or vice versa) (not books picking out really good versions of me to take home with them -- though that would be awesome -- but I read and my husband picks out books). But if you go just you and your three year old, she randomly picks things off the shelf that catch her eye and wants to read them then and there. Do you have a kid who will just sit quietly in the library and read to him- or (let's face it, probably) herself while you browse? Bless you.
As most writers are, I was a huge and wide reader as a child. So pre-parenthood, I could name lots and lots and lots of awesome books I remembered reading as a kid. That turns out not to be because kids' books are universally awesome but because I repressed the ones that weren't. I know this because D picks out books that MAKE NO SENSE where NOTHING HAPPENS and characters are POINTLESS and the whole thing feels phoned in and depressing. And I mean, these are children, you know? They're innocents. They deserve better. My ONLY goal when I read to D is to teach her to love books and reading. How can I do that if the books suck?
Narrative, people. Even children need narrative. Here are some new-since-I-was-three books we've found to love. What other newish and fabulous children books do you know?