From left: Rumer Willis, Annie Starke and Glenn Close on Jan. 28
01/30/2012 AT 12:30 PM EST
isn't letting family drama slow her down.
Following Demi Moore
's hospitalization last week
and decision to seek professional treatment
for exhaustion, her daughter – and frequent party companion
– was in full social mode, enjoying a busy weekend out and about in Los Angeles.
On Saturday night, Willis, 23 – who was apparently on hand
when Moore's friends called 911
after the actress had an apparent seizure
– stepped out for dinner at Comme Ça, joined by her friend Annie Starke, Annie's mother Glenn Close and Close's husband David Shaw.
Seated at a table in the front of the restaurant, the four ordered cocktails, clinked glasses and chatted. Rumer seemed happy and cheerful at times, but also sometimes looked concerned as though she were telling a serious story. Rumer held on tightly to her phone throughout the entire meal and frequently became engrossed in typing on it.
Rumer seemed "fine" an observer told PEOPLE. "She was sweet." The party of four "were all very gracious the whole time," the observer added.
Willis, Starke and Close spent Sunday evening together as well, at the Screen Actors Guild Awards
gala at the Shrine Auditorium, where Willis and Starke roamed the party and sipped champagne. They seemed particularly interested in checking out Brad Pitt
and Angelina Jolie
, making their way to the couple's area and watching as they were escorted out of the party.
Before making her exit, Rumer stopped to hug pal Mark Salling and got a kiss on the cheek from the Glee
actor. And Willis kept the party going, ending her night at West Hollywood's Chateau Marmont.
Reporting by PATRICK GOMEZ, MELODY CHIU and JESSICA WEDEMEYER