I definitely think she badgered Angel until he told her. He probably planned to tell her all along but just wanted to make her suffer a bit.

I don't know why it was never mentioned on-screen. Maybe the writers kept it vague in case they needed to fill it in later to make a storyline work. We never saw Willow find out about Connor but she definitely wasn't surprised by him when she showed up in L.A. in season 4. I guess a lot was happening off-screen.