AceShowbiz -

Alec Baldwin and his wife Hilaria Thomas finally introduce their daughter to the world, two weeks after the baby was born. "It's a second chance for me, in a way," Alec says. "Everybody knows I had a pretty unpleasant custody battle for Ireland," referring to his daughter from his first marriage to actress Kim Basinger.

Now that his first daughter, a model, is "well-adjusted and as happy as one can be," the former "30 Rock" actor is focusing his energy on devoting himself to the women in his life. "We just want things to be easy, to be nice," gushes the proud father of two to PEOPLE.

In a separate interview with Extra, Hilaria says of her little one, "Honestly, it's a dream come true. Every single day I have trouble sleeping because I just want to look at her, and every single day you wake up and it's Christmas." She adds, "It's a love that hurts. I want to make sure she's okay, every single step of the way... it's just absolutely indescribable."

Of who baby Carmen looks like, Alex jokes, "I hope she looks like her mother. What a waste of time it would be to marry a woman like that and have the kid look like me." Meanwhile, his wife says, "She looks like herself... we'll have to see, every single day, she changes so much."

"She sleeps like a rock all day. And at night she's like, 'Let's have a conference,' " Alex additionally spills, to which his yoga instructor wife jokingly adds, "Now I'm getting to the point where if I don't sleep, I'm going to start walking into walls."