Hudson sang Saturday night at a theater in Chicago's McCormick Place.
She dedicated the song "You Pulled Me Through" to relatives in the audience and brought four cousins on stage to sing with her.
The bodies of her mother and brother were found Oct. 24 at their home on Chicago's South Side. The body of nephew Julian King was found days later on the city's West Side.
The estranged husband of Hudson's sister, William Balfour, is charged in the murders.
Hudson is in the middle of a tour with singer Robin Thicke.
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