I'm going to answer your questions one by one ....
Who are Princess and Ivy? Are they related? Where is Dad?
Princess is the mother at the Radisson Hotel nestsite here in Winnipeg and Ivy is her mate this year - he's a bit younger than she is but he's the daddy of this year's chicks. Actually, he has been the daddy at this site since 2010 and Princess has been the Mum here since 2004 - her mate before Ivy was Trey but he didn't come back to Winnipeg in 2010 and so Ivy became Princess' mate.
Now you are probably saying that Ivy is a pretty funny name for a male peregrine, and it is if you don't know how he got his name. Now your teacher is going to have to help you out with this - maybe on the blackboard or on the computer because its easier to explain if you draw it out. The first male peregrine at the Radisson was Pop and the second male was Pop's son who's name was T-Rex (because he was very fierce and scary, but we liked him alot). The third male at the Radisson was Simba but he wasn't T-Rex's son, he was his nephew from Brandon, which was kind a cool. The fourth male at the Radisson was Trey and he was T-Rex's son. Trey's got his name because he was the third generation of Radisson males - he was the son of T-Rex and the grand-son of Pop. Ivy is the fourth generation - he is Trey's son, T-Rex's grandson and Pop's great-grandson. For example, if my name was James and my father's name was James, people would call my father James Senior and me James Junior. Now if everyone in my family was called James, then my great-grandfather would be James I, my grandfather would be James II, my father would be James III and I would be James IV. Sometimes people with III after their name are called Trey (like Ivy's Dad) and people with IV after their name are called, you guessed it, Ivy. And that's how Ivy got his name.