Best Answer - Chosen by the Asker
The sentence should be rephrased a bit. You are correct in thinking it would be better to say "...a teenage son and a daughter" or "...two children: a teenage son and a daughter." This states that you have one son in his teens and one daughter whose age you did not specify. If both children are in their teens, you could state: "I am a housewife with two teenage children: a son and a daughter." Saying "a teenage son and daughter" doesn't make it completely clear which of the two statements you're trying to make, even if it is clear that you only have one daughter.
The best way to see if you need to specify a quantity would be to make multiple sentences and see if each sentence is correct. For example, if I break your sentence down into "I am housewife with a teenage son" and "I am a housewife with daughter," it's clear the second one isn't grammatically correct. It should be "I am a housewife with a daughter" or "I am a housewife with one daughter."
Notes for expressing the quantity of countable objects:
* If the object is singular you should use 'a' or 'one' (e.g. "I have a table" or "I have one table")
* If the object is plural, you should add an 's' at the end of the word. You can then decide whether or not to express the exact quantity of the object (e.g. "I have tables" or "I have three tables.")
