"The form tercer is only used before and within the noun phrase of the modified masculine singular noun. In other positions, the standard form tercero is used instead." -- http://en.wiktionary.org/wiki/tercer#Usage_notes_2
Of course, I don't really understand what that means ...
Haha, you're right! What don't you understand? If tercero (or primero) is an adjective preceding a masculine singular noun (take 'the third son' for example), there is no -o on the end. He is 'el tercer hijo.'
Ordinal numbers used as adjectives almost always precede the noun, so you should get used to knowing to drop the -o when primero or tercero are adjectives. Some exceptions are royalty/popes... Important people who are known by titles such as Edward I (Edward the First/Eduardo Primero de Inglaterra). The ordinal number used as an adjective follows the noun in these cases.
Now, if the ordinal number is used as a noun: my son is the third (one) is 'mi hijo es el tercero.' It isn't being used as an adjective before a masculine noun* here, so it keeps its -o.
Hola Talca: I am wracking my brain to think of the word. There IS a word of endearment for the youngest daughter, but it is not coming to mind. If I think of it later, I will try to get back to you. I have a friend in Hondura swho uses it all the time, but I can't think of it. In the meantime, one way to say it is "Mija" which is a contraction of "Mi hija" or more diminutive: "Mijita" which is a contraction of "Mi hijita". AHHH!!! Light Bulb went off/////////////; I think the other word is "tierna"; I am not 100% sure, but I am pretty sure that "tierna" in Spanish is the equivalent of "benjamine" in French.
The son/child issue shouldn't be the problem here. Hijo can pretty much always be translated to either.
But instead you changed the structure of the sentence. You went from "He is the third of my children"/"Él es el tercero de mis hijos" to "He is my third child"/ "Él es mi tercer hijo".