Hi, I'm sorry it took me so long to answer 😅
One of my favorite things about the saga is that the role of the mother is not sanctified. Suzanne writes mothers with flaws, virtues, and making mistakes but without forgetting that they are also victims of the system and how it affects them. (Mrs. Everdeen by being a healer who has seen the consequences of violence from authority figures, her depression, and her ability to teach Prim. And Mrs. Mellark with her closed-minded and cruel way of looking at the world).
I think Peeta and Katniss' childhood and their relationships with their moms is a very sad topic but so real that it hurts. They both actively try not to be like them. They despise or try to eliminate the "core" characteristics of their moms that they find in themselves. Katniss by repressing her feelings because she thinks they make her weak, and Peeta with his need to keep an iron grip on his reactions. The tragedy is that when they are at their lowest and most helpless moment, they become mirrors of their mothers. But I think, in some ways, it is because of their mothers that they survive everything the story throws at them.
Katniss survives the district thanks to the knowledge she inherited from her father, but she survives the games and the war because of her ability to do what it takes to protect/save others, which she inherited from her mother. It's something all three Everdeen women share. Peeta often tells her "You're the healer" and Katniss always contradicts him, but the truth is that Katniss also shares that gift. She just doesn't see it because, for her, the image of healing is Prim.
Peeta survives the capitol (in all its forms) due to what he learned from his mother, from reacting under pressure to smiling when he's choking with fear. Something little talked about is that one of the reasons Peeta makes it back from the hijacking is because of his mother: She gave him the experience of what it is like to love someone who causes him fear.
Perhaps my point of view is cliché or simple when analyzing Katniss and Peeta's mothers but I think their depth and humanity lie precisely in how they influenced their children and how "simple" it is for us to understand and empathize with the children early on and then understand and empathize (or not) with their mothers as we grow up.
[When translating this answer I feel I rambled a bit so I apologize for that hehe].
It was a wonderful question! Thank you for sending it 😊