I'm unsure whether this as an answer is within the rules, but I think you're reading too much into it. Contrary to popular belief in their decline, political cartoonists of the 20th century weren't hesitant with labels - as examples by the contemporary anti-fascist Theodor Geisel (better known as Dr. Seuss) will show. The principle of labelling - basically to label anything or anyone that isn't immediately obvious to the reader, especially nebulous social or political factors - applied just as much then as it does today.

Meanwhile in my readings on Italian fascist history I know of nothing that was commonly analogised to a "Mussolini Jr." If it was a particular person or movement, the cartoonist would have almost certainly labelled it.

The humour in this comic to interwar-era English speakers would rather come from popular perception of Mussolini's rhetoric. The Fascist ultra-nationalist concept of Italia Irredenta, by which Italy was entitled to all land with an Italian population or which Italy had any kind of historical connection to, made for a particularly inflammatory rhetoric which challenged the borders of the entire Mediterranean and even the concept of nation-state in general. This rhetoric was foreign to most native English-speaking populations (for whom most national border disputes had been settled in the previous century or long before), and I'd wager that the humour of this cartoon comes from the idea that irredentism is nothing more than the mood swings of a new father.

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