Kathy Hilton Shares Message of Support for Sister Kim Richards amid Her Relapse: 'We Love Her' (Exclusive)

Kathy Hilton is sending sisterly support to Kim Richards .

Hilton, 65, gave PEOPLE a brief update on Kim, 60, who reportedly has been struggling with substance use , on Saturday, Oct. 5, during the Rebecca Vallance x Nicky Hilton Holiday Collection Celebration event hosted by MyTheresa at Hilton's Los Angeles home.

"We love her and we support her, and that's all I can say," Hilton said.

Asked if Kim is doing better, Hilton replied, "Yes," before adding that "I think in the world there's always hope."

Kim's addiction struggles have been documented through the years, including in 2010 when her sister Kyle Richards , 55, revealed her to be an alcoholic on Real Housewives of Beverly Hills. Kim entered rehab the following year , and also spent time in rehab in 2015 after being charged with public intoxication .

In September, TMZ reported that Kim was staying in a Hilton Hotel earlier that month and was then placed on a 5150 psychiatric hold and taken to a hospital following "incoherent" behavior. Once she was released, Kyle offered to take her into her home.

Soon after, on Sept. 25, the Los Angeles Police Department confirmed to PEOPLE an incident occurred in the Encino area, where a source told PEOPLE Kyle owns a home that Kim had recently been staying in. The LAPD said officers responded to "keep the peace" after a female reportedly violated a restraining order but they then determined there was no order on file and no crime was committed.

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TMZ also reported that Kim's family had cut contact with her, hoping that she would possibly get sober again while being shut out.

A source told PEOPLE in September that Kim's "reliance on alcohol has been an ongoing source of conflict between her and her sisters."

"It particularly weighs heavily on Kyle, who has always been the worrier of the family," the insider added. "She does her best to take care of Kim — and essentially bankrolls Kim's life, with Kathy — but never knows where the line goes between helping and enabling."

Kim's family acknowledges that the reality star is in "a really bad place," but aren't speaking about the situation.

"The family are very private about details, but from the little they've said, it's clear they've reached another breaking point with her," the insider added, emphasizing that "this has happened before."

"It's the same cycle: chaos until there's some incident that gets Kim back on track, then brief steadiness as they repair their relationship, then the drinking starts again, Kim makes excuses, Kyle pleads she gets help, etc., etc."