If there are three children in the family:
A. a boy, eldest
B. a girl
C. a boy, youngest
Is it correct for their father to refer to A as 'my eldest son' and to B as 'my younger daughter'? If not, what expression would be preferred? Thank you.
If you compare two people you should use only the comparative form of the adjective (in your case 'my elder son').
The alternative form can be 'my eldest child' as you compare three people here. This is the superlative form of the adjective.
As about the daughter you just say 'my daughter'.