'my eldest son'

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 for the daughter, you just say ‘my daughter’.

You have two sons so it's better to say "my elder son". If you have three sons, however, you would say "my eldest son" because if you say "my elder son", people will assume you have two sons and not three.

As you only have one daughter, it would be wrong if you said "my younger daughter" (as you don't have a daughter that is older than her). You should simply say "my daughter".