Hilaria Baldwin says family 'spending lots of time together' amid Rust shooting fallout

Hilaria Baldwin is checking in with fans as she and her family continue to cope with the aftermath of husband Alec Baldwin's accidental shooting on the set of his movie, Rust.

On Sunday, the fitness influencer, 37, shared a video montage of photos of her and Alec, 63, spending time with their six 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.

"Check in," Hilaria captioned the post. "Spending lots of time together. Grateful for these kids. Grateful for you 💕"

The images included a photo of a family hike and a picture of Alec cradling one of their youngest children.

The mom of six shared a similar update last Sunday, writing alongside a different montage, "Checking in and sharing a few moments. Being together. I know you worry. We love you and miss you."

RELATED: Alec Baldwin Sued by Rust Gaffer Who Claims Actor and Film's Producers Were Negligent with Firearms on Set

Alec's accidental shooting, which killed cinematographer Halyna Hutchins and injured director Joel Souza, occurred Oct. 21 on the Santa Fe, New Mexico set.

Never miss a story — sign up forPEOPLE's free daily newsletter to stay up-to-date on the best of what PEOPLE has to offer, from juicy celebrity news to compelling human interest stories.

alec baldwin, hilaria baldwin
alec baldwin, hilaria baldwin

Hilaria Baldwin/Instagram

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 Alec knew that the gun had live ammunition in it, according to the affidavit.

Hilaria Baldwin and Alec Baldwin
Hilaria Baldwin and Alec Baldwin

Jamie McCarthy/Getty Hilaria and Alec Baldwin

RELATED: Alec Baldwin Calls on Hollywood to Have a Police Officer on Sets to 'Monitor Weapons Safety'

Hilaria has also previously spoken about the challenges of parenting in the aftermath of the incident.

"Parenting through this has been an intense experience, to say the least. Today, we rallied to give them a holiday," she captioned a post of photos of the family celebrating Halloween last month.

As local authorities in New Mexico continue to investigate the tragic accident — with production on the film halted — a source told PEOPLE that Alec is leaning on his wife and kids to get through.

"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."

Advertisement