I'm not actually sure if there is a way to tell who the dad is. Although I have seen my Sim tell the father right away in a few of my games, but only if he is on the same lot. Another time when the father wasn't there, she didn't say anything to any other Sim in the household.
As for not knowing or caring, yeah they don't care really. I've never had a male Sim have a negative moodlet of any kind when, say, his wife gives birth to another Sim's child. It's like it never happened lol. They only seem to get jealous when they see flirting with other Sims.