It certainly used to be a rule, but there are grounds for ignoring it. This would be strongest where you were uncertain of the number of children (not the case here). But you can certainly argue that in logic, there is an oldest of 1, 2, or more children. So, your mother is almost certainly correct about what she was taught. Whether that stricture still has to be followed is considerably more debatable.
I think John Lawler and others make a good point in that "antonyms" are vague, and I suspect that, despite the descriptivist intent, the question arises from a semantic issue.
From Wiktionary, an antonym is "a word which has the opposite meaning of another, although not necessarily in all its senses." Thus fast is an antonym of slow, but fast is also an antonym of eat. However, most of us wouldn't think about comparing speed with consumption. Useful can be interpreted as "having non-zero utility," which means the opposite of useless. However, useful can also mean "having a positive degree of utility" which is not the opposite of useless. So they are fine antonyms, but not opposite in all meanings. A more appropriate opposite for the comparative version of useful would be harmful or detrimental.
For the more descriptive questions, specifically regarding the "-ful" and "-less" suffixes, I suspect that use of these words depend on how these suffixes are commonly interpreted. "Doubtless" and "useless," for example, imply devoid of doubt and devoid of use. "Thoughtless" and "tasteless," for example, imply lacking thought and lacking taste. The latter pair would be more common in comparative relative to non-comparative use since one can be naturally seen as more or less lacking. The former pair is less commonly seen since it is less logical and descriptively less common (though not unthinkable) to be seen as more or less devoid (of course, cf. emptiest). In general the commonality of use seems to me in line with whether or not it is logical -- so I don't see them as necessarily in conflict.
However, one exception comes to my mind (not saying that there aren't others). When raukh mentioned "impossible" (p = 0), my first thought of an antonym was "certain" (p = 1). As someone more accustomed to speaking with statisticians, for me, it sounds awkward when someone says something is more or less certain. However, I recognize that both descriptively and formally, certain is a comparative adjective. Indeed, it seems that the use of certain as a comparative is more common than the use of uncertain as a comparative, although that appears to be in relative decline.
Additionally -- this is perhaps silly of me to think it needs stating -- choice of which words to use also depend upon the emphasis of the sentence, even for paired words. Whether someting is "more impossible" or "less possible" may, for some, have different connotations. Curiously, those words seem to be converging in frequency of use.
Best Answer
The two children are members of a group and the comparative or superlative relates to that group.
Expressions like the ten best universities or the cleverer children in the class are quite common and I don't think require further explanation.
As for her two younger children, both forms are grammatically acceptable but I prefer her two youngest children because it is clear that the superlative implies comparison to the entire set. Use of the comparative, on the other hand, brings some confusion, because there is some ambiguity as to whether there exists a younger child than the two present, although I would probably assume this is not the case. We also have to disregard a potential comparison with the woman herself, which would be a pleonasm.