How do we trade-off succinctness for accuracy in 每当我爸忙的时侯他就让我吃?
我爸忙时(他)就让我吃 is a correct translation for When my father was busy, he would let me eat ....

But I guess your intended meaning is probably: When my father was busy, he would not forbid me from eating ..., 我爸忙时(他)就不管我吃东西