The proudest moment in Grace O'Malley's life, aside from being a mother, was when she joined the culinary workers' union in 1951.

The saddest times, she says, have been in the current strike against hotel- casinos here. The three-week-old strike has interrupted her eight years as a Caesars Palace waitress and put her and 17,000 other hotel workers out on the picket lines: waitresses, bartenders, stage hands, fry cooks, bellhops and people in the host of other jobs that go into running the 24-hour neon fantasy that bills itself as the entertainment capital of the world.

''Working in Las Vegas is like belonging to a family, where you know everybody,'' says Mrs. O'Malley. ''I've always been proud to say I'm a Caesars employee, but now I'm ashamed of what they are doing to us.''

The 32 hotels that remain struck by the culinary workers', bartenders', musicians' and stagehands' unions are themselves caught in uncertain times that have deeply affected the strike.