Hi Elizabeth,
Can you post a sample or example of what your characters are trying to convey for us to look at?
Generally, for a picture book, I would always include dialogue tags:
"Did you pick the apples?" asked Mom.
"Five of them," said Bob.
"The green ones?" asked Dad.
"No, the red ones," said Molly.
"But I wanted pears!" said Bill.
I find when I am reading picture books to my 2-year-old, I add dialogue tags where there aren't any for clarity, but a book for an older child might be OK just with context.