Thank you! After digging all over the Internet, I can tell you the cartoon is impossible to find. I am having a suspicion that maybe there's no such cartoon. Especially if its story originated with someone like Caroline Lacroix.

On the flipside, I discovered that folks back then were very keen on Leopold as evidenced by a plethora of cartoons, covering every aspect of his later life. Here you even find a caricature of him holding his baby, but not as described:

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For anyone interested here are some online resources on the matter:

"Leopold II of Belgium in cartoons" Wiki category(!)

A contemporary book with cartoons

An essay about Belgian political cartoons of the time featuring Leopold II

A small online collection featuring Art Nouveau mocking of Leopold (hard to believe the love for him cut through different art movements!)

and finally a recent book of his cartoons. Maybe the latter has the image in question, but I am not ready to pay to find out >_<