Prim and Katniss' mom are more important for what they mean to Katniss than for what they do in Catching Fire. They're both love Katniss, but they're also powerless to do anything to help her. Katniss usually has to take care of her mother, but when the need arises, her mother steps forward as a responsible caretaker:
I'm filled with awe, as I always am, as I watch her transform from a woman who calls me to kill a spider to a woman immune to fear. When a sick or dying person is brought to her… this is the only time I think my mother knows who she is. (8.39)
Still depressed by the loss of her husband, Katniss' mother retreats into herself when she doesn't have a patient to heal. She keeps to herself so much that we don't even know her name.
As in the first book, Katniss has to be the responsible adult in the household and take care of her sister. Prim is probably the person Katniss loves most in the world, and Katniss is terrified of losing her, as we see during Katniss' run-in with the jabberjays that imitate Prim's voice:
I run wildly in the direction of the voice, heedless of danger, ripping through vines and branches, through anything that keeps me from reaching her. [...] From reaching my little sister. (23.79-80)
Katniss loves her family and would do anything to help them. It simplifies things that there's no conflict within her family in Catching Fire. She never has to choose between her mother and her sister in the way it seems she's always being pushed to choose between Peeta and Gale.