"We want more -- as many healthy kids as God blesses us with," shares Daly.
But off-camera, Daly’s main focus is his family: fiancée Siri Pinter, 32, and the couple’s two children, Jackson James, 4½, and Etta Jones, 16 months.
“After this many years, I know who I am. My life is not television,” Daly, 40, tells PEOPLE exclusively. “I’m a family man first and foremost. Everything I do in this business, it all pays off when I come home.”
And with a self-proclaimed “insane” life — it’s packed with his own radio show, his late night talk show, Last Call, and a gig on Today — home life is also Daly’s cherished escape.
“Our family time is like happy hour,” he says. “Siri and Etta are cooking and I’m making kiddie cocktails with Jack — that’s our thing.”
After being introduced to Pinter while she was working as a writer’s assistant on Last Call — “She would walk into our meetings and I would look at the other dudes in the room, like, ‘Do you see what I see?’ It was undeniable” — Daly proposed last June. But he and his food blogger fiancée aren’t in a rush to tie the knot just yet.
“Our lives have been crazy,” he explains. “We’ll get married when we have time. The husband and wife thing is just the bow around something. Our end game is we want to be together forever.”
And they haven’t closed the door on expanding the family. “We want more — as many healthy kids as God blesses us with,” shares Daly.
But, until then, the couple is kept plenty busy with their “whiz kid” Jack, who is often trailed by his baby sister. “[She] runs and jumps and follows her brother around,” the doting dad says.
Thankfully, The Voice set is a kid-friendly zone.
“My son and Christina [Aguilera‘s] son play together,” says Daly with a laugh. As host of MTV’s TRL in the ’90s, he often interviewed the pop superstar. “We sit there and look at them playing and say, ‘Can you believe this? Look at us now!'”
For more from PEOPLE’s exclusive interview and photos of the family, pick up the Half Their Size issue.
— Aili Nahas