Unbaptized infants are not separated from God naturally, but only supernaturally.  That is why Limbo is a special case, because it's different from the rest of hell.  As for Limbo being part of hell, vs. its own thing, that is speculative anyway.  There are so many holes in this, that it's not even funny, the first one being the use of CCC as if it were some reliable guide to faith.

The Second Council of Lyons: “The souls of those who die in mortal sin or with original sin only, however, immediately descend to hell, yet to be punished with different punishments.”

The Council of Florence: “But the souls of those who depart this life in actual mortal sin, or in original sin alone, go down straightaway to hell to be punished, but with unequal pains.”

I'm aware catechisms are fallible, but I thought that particular teaching was universally thought - I just wasn't aware of the distinction between a natural vs supernatural separation from God.
As for Limbo being part of Hell, that's probably dogmatic if you consider the following:
All souls marked with original sin go to Hell, that appears to be dogmatic. The idea of Limbo of the Infants is that it's a part of Hell reserved for those who only have original sin, and therefore do not suffer as per the "unequal pains" part of each dogmatic definition above.

The natural vs supernatural distinction you mentioned does seem to be the refutation of the writer's argument though, so could you expand on that please?

It should be added that in St. Thomas' view the limbus infantium is not a mere negative state of immunity from suffering and sorrow, but a state of positive happiness in which the soul is united to God by a knowledge and love of him proportionate to nature's capacity.

Finally, in regard to the teaching of the Council of Florence, it is incredible that the Fathers there assembled had any intention of defining a question so remote from the issue on which reunion with the Greeks depended, and one which was recognized at the time as being open to free discussion and continued to be so regarded by theologians for several centuries afterwards. What the council evidently intended to deny in the passage alleged was the postponement of final awards until the day of judgement. Those dying in original sin are said to descend into Hell, but this does not necessarily mean anything more than that they are excluded eternally from the vision of God. In this sense they are damned; they have failed to reach their supernatural destiny, and this viewed objectively is a true penalty. Thus the Council of Florence, however literally interpreted, does not deny the possibility of perfect subjective happiness for those dying in original sin, and this is all that is needed from the dogmatic viewpoint to justify the prevailing Catholic notion of the children's limbo, while from the standpoint of reason, as St. Gregory of nαzιanzus pointed out long ago, no harsher view can be reconciled with a worthy concept of God's justice and other attributes.

Before I go further, I will just say speculation, speculation, this is all speculation.

Is it not possible that those in limbo enjoy a "perfect natural happiness" but do not suffer, because even though they do not possess God, they do not know that they are lacking in anything?  Could it be like someone who lives on a beautiful seashore, the weather is perfect 12 months a year, any rainfall is light and pleasant, no natural disasters, abundant food and drink, pleasant natives, always in good health, like the finest Club Med you can imagine.  They go around day in and day out thinking "life is good" and want nothing more, because they are not aware that there is "something more"?  That there is a perfect city over the horizon, out of sight, and there is high culture in abundance, endless opportunities for enjoyment and improvement of oneself, the most enjoyable and fulfilling social relationships imaginable, and delights that make their "Club Med" look like a rundown beach hotel?  It exists, but they don't know it.  Is that a possibility?

As for Limbo being part of hell, vs. its own thing...