"Younger" or "youngest"

Solution 1:

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.

Solution 2:

Well, lets suppose you have 3 kids- 13, 9 and 7 years old. Then 7 years old is the youngest child, 13 years old is the oldest child, 13 and 9 years old are the two older children and 7 and 9 years old are the two younger children. This is not question about language but rather a question about sets to me. When you are talking about the youngest or the oldest, that should be only one of that kind. The answer that makes sense here is younger.