Hilaria Baldwin shared photos and home videos of her six children as the family spends time in Vermont

Hilaria Baldwin is keeping fans in the loop.

On Instagram Sunday, the 37-year-old fitness influencer shared an update about how her family is doing as they cope amid the accidental shooting on the set of her husband Alec Baldwin's film Rust.

In the photo and video montage, the couple's children — daughters Carmen Gabriela, 8, and María Lucía Victoria, 8 months, and sons Rafael Thomas, 6, Leonardo Ángel Charles, 5, Romeo Alejandro David, 3, and Eduardo "Edu" Pao Lucas, 13 months — played and laughed together.

The clip included shots of cows, llamas and fall foliage, and closed with a photo of the 63-year-old actor holding María Lucía.

Hilaria Thomas Baldwin Instagram
Credit: Hilaria Thomas Baldwin Instagram

"Checking in and sharing a few moments. Being together. I know you worry. We love you and miss you," Hilaria wrote in the caption.

Hilaria Thomas Baldwin Instagram
Credit: Hilaria Thomas Baldwin Instagram

A source told PEOPLE that the Baldwins are currently "laying low" in Vermont following Alec's accidental shooting on the Rust set, which killed cinematographer Halyna Hutchins and injured director Joel Souza.

"Alec and Hilaria left the city and are laying low with the kids," the source said. "They do go out occasionally to pick up dinner, but are mostly trying to protect the kids' privacy and just spend quiet time together as a family."

Last week, Hilaria described parenting in the aftermath of the tragedy as an "intense experience" following the on-set accident, posting photos of the family dressed up in "last min" costumes for Halloween.

Hilaria Baldwin and Alec Baldwin
Hilaria and Alec Baldwin
| Credit: Jamie McCarthy/Getty

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The accident occurred on Oct. 21 in Santa Fe, New Mexico, on set of the Western starring Alec and directed by Souza.

During a rehearsal, assistant director David Halls unknowingly handed Alec a gun that had been loaded with at least one live round. Thinking it was only loaded with blanks, Halls shouted "cold gun" to indicate it was safe to use, according to a Santa Fe County Sheriff's Office search warrant affidavit.

Alec shot the Colt .45 revolver, which fatally injured Hutchins and hospitalized Souza. Neither Halls nor Baldwin knew that the gun had live ammunition in it, according to the affidavit.

Alec Baldwin attends the World Premiere of National Geographic Documentary Films' 'The First Wave' at Hamptons International Film Festival on October 07, 2021 in East Hampton, New York.
Alec Baldwin
| Credit: Mark Sagliocco/Getty

As local authorities in New Mexico continue to investigate the tragic accident — with production on the film halted — another source told PEOPLE that the three-time Emmy Award winner is leaning on his wife and kids.

"It's such an unthinkable tragedy and the grief and trauma for him are unbearable," the source said. "Alec is still in shock and his heart is completely broken. He is doing his best to cope and is leaning on Hilaria and the kids for support." 

Days after the accident, the mom of six posted a photo holding her husband's hand, captioning the snap, "I love you and I'm here❤️."