Probably published in the 1950s or even the late ’40s.  Maybe in Britain or Canada.
Children’s fantasy/detective story

Plot: A single (gasp!) mother (probably a war widow) with 2 kids, a boy and a girl.  She is being courted by the neighbourhood beat cop.  The kids want to buy her something special for her birthday and they have saved their allowance so they have enough to buy her a small second-hand radio.  The kids know she loves music and dancing.  Kids find out later that radio is magic and broadcasts crimes in progress, which they , of course, try to stop/solve, and get their bacon saved by the cop character. I know this is a faint, faint hope. But it was such a change from Dick and Jane, which I refused to read aloud, thus grade one ended with me being labelled as mentally deficient. It was astoundingly different from anything else I ever saw until I was in my teens.Best of Luck to you – and for me!