You have to keep in mind that you're looking at two thinking, feeling adults that have capitulated in their struggle to conform to social norms. I know it's hip to pretend that fat people enjoy sweating when they go up a flight of stairs and having to sprinkle Gold Bond in their crevices to forestall dermal yeast infections but fundamentally we're talking about people who have given up on normalcy. They have, as a consequence, adapted to other coping strategies to live their lives to their own best abilities. They teach their children these strategies not because their behavior is "disgusting and unconscionable" but because it is the culmination of their life experience. They concluded at some point that their children would live as they do, much to their heartbreak, and so they are propagating the wisdom of the tribe. Mt sister's kids look like a Gap ad. They're impossibly thin. My own daughter will, if she's lucky, be built like Lucy Lawless. She's five but I already know that I will raise her to be her, not my sister's kids. Don't make me tell the story of the bamboo skewer.
My assumption is basically that they live like that and raise their children like that because a) they don't know better (about nutrition/eating properly), b) they don't care/don't have the energy to tackle the problem. Some combination of the above. I'm sure they had a lot of other things going on in their lives too. As someone who doesn't have kids, I feel like the timesuck of having multiple children and raising them "well" in all the other vectors a person might possibly want to raise their children well in - quite reasonably reduces the amount of time and energy a parent can direct towards self-improvement. Or changing what's always worked for them. Or teaching their children an entirely different lifestyle from what the parents know and live. It'd require a re-self-education and then application and re-teaching of that new knowledge to 1, 2, however many children. And even if you can change the lifestyle, the kids already absorbed what life was like before the change for however long that was. I just felt really bad for the younger kid. who was obese at like 10. Sure, sometimes people seem to raise perfect kids, but for the most part I think it's impossible. You can raise your kids as best as you can and that's about it. Even just a blind spot in the 'wrong' vector -- any possibly significant vector, which is like almost all of them -- can leave a kid vulnerable or disadvantaged. Guess what! That's being human for ya. I don't know any adults who are perfect (in my life, anyway). Why expect parents to produce children who excel in every way and are in control of and smart about all their choices, when the parents aren't like that and also no one in society really expects that of them?
Your a/b is actually an a/b/c; don't know better/don't care/ don't have the energy might all be of a kind at first glance but it's a can't/won't/can't. It's not a can't/can't/can't. And that, right there, is the fundamental issue - externally, everyone here is arguing that fat people are fat because they can't or won't change (same diff) while internally, fat people are 100% all the time at "can't" or, more accurately, "have tried fucking everything and who the fuck do you think you are implying my can't is a won't". And the answer is always some form of "someone calling you fat, fatty, what the fuck are you going to do about it." Above, you're basically saying "these people can't or won't take care of their children." And while you might get agreement on "can't" (be it grudging, despairing or defiant), you will never ever ever convince someone they won't take care of their kids. Especially when you're arguing that allowing them to look like their parents is child abuse.