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.
His sister is his youngest sibling, but his younger sister. Since she is the lone female child, there is no need for the superlative form. Suppose, however, that there are more siblings, and their birth order goes like this: boy, girl, boy, boy, girl.
my [young / younger / youngest] sisters - English Language & Usage ...
An only child is both the youngest and the oldest, sure. But you cannot say "the youngest of the two children", now can you? You would never ask someone which of their parents was the oldest. It just doesn’t feel right. The older parent is older than the other, since you can’t say that the oldest parent (of the two) is *oldest than the other.
He was one of the youngest of his siblings. The meaning should be clear: he had many brothers and sisters, and he was one of the youngest of the lot, but the expression feels awfully awkward to me, with expression his siblings implicitly excluding the subject from the set; you're not your own sibling, so you're not one of your siblings.
But phrases like “my youngest younger brother”, “my youngest older brother”, “my older younger brother”, “my younger older brother”, and “my oldest younger brother” all serve useful purposes in different cases.
If you only have one sister and she is younger than you, she is your younger/little/baby sister. If you have several sisters, it gets more complicated: The sisters closest to you in age, but younger, are your younger/little sisters. The youngest sister is then your "baby sister". (US)