Younger vs. youngest

Younger for comparison of two of the same kind of thing, youngest for more than two of the same kind of thing. Your husband seems to be combining his "youngest child" and his "daughter" in a sort of portmanteau shorthand that doesn't logically follow. If I were you I'd smile indulgently at him and tell him unless he doesn't have another daughter you don't know about somewhere, and as long as your son isn't an XX, you'll let him mangle the language to his heart's content.

This is known as the superlative of two. There's nothing wrong with it. Merriam Webster's Dictionary of English Usage gives examples (page 881). The Columbia Guide to Standard American English notes that in speech there's nothing wrong with it.
http://www.bartleby.com/68/43/5843.html

Sorry to say that Delia is wrong, but John is right. You can say Rebecca is the younger of my two daughters or Rebecca is younger than daughter B, (both comparision mode) and Rebecca is my youngest daughter (superlative). And since Rebecca is your youngest child of two girls and a boy, you can, of course, say Rebecca is my youngest child (and youngest daughter). We've to be specific when using the English language otherwise ambiguity creeps in. FYI, I'm a linguist and language tutor who teaches English, French, German and Spanish.

Well, beans to Jonah and the Columbia Guide to Standard American English! I'm a purist and I stand behind both Cheri and Delia!

I would say that this is not an issue of "purity" as much as it is an issue of clarity. Should you say she is the youngest daughter, and your audience, by some means, becomes aware of the existence of another child--obviously a male--then it creates an unwelcome emphasis which might lead your listener to believe the daughter is a middle child. The most precise manner to express this is as you suggest, Cheri.

As for the "purity" of English, we've all got out pet peeves, but we must face the undeniable fact that our language is not the same language that is was even ten years ago. The truest form of purity in this case is to adapt as it changes. Were we to live quite miraculously to 500 years and maintain "purity" or speech, we would be utterly unintelligible to our listeners.

"My older brother" can refer to either a brother who is older than me or who is younger than me. Just the same as "my oldest brother." It all has to do with context. You can use the superlative of two and be just as clear or just as not clear as not using the superlative of two.

MW Dictionary of English Usage:
The common assertion of the grammarians, that the superlative degree is not applicable to two objects, is not only unsupported by any reason in the nature of things, but is contradicted in practices by almost every man who affirms it.

You are correct, your husband is wrong.
"er" is in comparison of two of the same type, while "est" is used to compare three or more of the same type.

Of course, in math, is it not considered at all incorrect to have a superlative of one: "zero is the smallest integer which is neither positive nor negative". Or even superlative of zero: "The smallest integer which is both positive and negative does not exist".

I remember as a kid being told that there are some languages in which there are only three numbers: one, two, and "many". I thought that was rather odd, but it turns out that grammatically speaking, English is such a language: "she is my young daughter" (one), "she is my younger daughter" (two), "she is my youngest daughter" (many).

Jonah:

That's odd. Are you unaware that contracting "have" when it's not being used to mark perfection is highly nonstandard?