Amy - who met Darren in acting class in 2001 - told the USA Today newspaper: "I love that balance. I had a talk show blitz the other day.
"I had three hours down, so I raced home, changed out of my nice clothes and we walked to Central Park (in New York City) and did the merry-go-round because I promised her we'd do it before we went back - and she remembers. And then we walked back."
The 38-year-old redhead also revealed Aviana is a very strong-willed child and she doesn't even like to be comforted by her mother when she is upset.
Recalling a flight when Aviana wouldn't stop sobbing, she said: "It's funny. She doesn't like to be held when she's upset. She's very independent. This one woman kept going, 'Why doesn't she just pick her up?' It's like, 'Do you know what would happen if I tried to pick my child up right now?' She would lose her mind. I probably shouldn't worry about it. I love my child."
With a busy year ahead promoting three very different films - 'The Master', 'In Trouble with the Curve' and new Superman movie 'Man of Steel' - Amy sees each project as an exciting adventure and enjoys seeing the final product on the big screen.
She explained: "It's like having a 'this is your life' moment. This is what I spent the last two and a half years doing.
"It's wonderful and so surreal. The experience of making the film is always the special part."