updated 01/31/2014 AT 1:00 PM ET
•originally published 01/31/2014 AT 2:30 PM ET
Ireland Baldwin looks to be smitten with her baby half-sister.
“Spending my morning with chubby bunny,” Ireland captioned the adorable snapshot.
The photo comes after a tumultuous week for little Carmen, who Alec claims was “patted down” by airport security in the Bahamas on Monday. Ireland also criticized the process, Tweeting, “I don’t know why I always get special checks at airports. Am I really that sketchy?”
Travel woes aside, the family has been enjoying spending time together in New York City, where Alec, Ireland and Hilaria attended Bent on Learning’s annual Inspire! Gala.
“It’s a second chance for me, in a way,” Alec has told PEOPLE of daughter Carmen’s birth. “Everybody knows I had a pretty unpleasant custody battle for Ireland.”
For her part, Ireland was thrilled to welcome a new baby into the Baldwin brood.
“You have been born into one crazy family,” she wrote on Tumblr. “We are going to have so much fun together I promise you I will always be there for you no matter what!”