Two of the five of us in our family with MitoD have what might be described as ARFID. "Avoidant/Restrictive Food Intake Disorder (ARFID), also known as “extreme picky eating,” is an eating disorder characterized by highly selective eating habits, disturbed feeding patterns or both. It often results in significant nutrition and energy deficiencies, and for children, failure to gain weight." OK, here is my family that needs to eat healthy due to the MitoD and two of them won't eat anything but junk (and only certain junk food) for the most part because of a fear of eating certain foods. Things I hear are -- it looks wet, or disgusting, or the texture will make me sick.... It doesn't matter if we go out, or if it's a family dinner, or if they are eating at friend's houses these two eat little good food. I understand ARFID is more common among the autistic spectrum and OCD community. Is is also more common among Chronic Fatigue patients?
How old are your kids? If they are young, I wouldn't cater to them. Buy the foods you think they should be eating and leave the 'junk' for special occasions. And if they are older, if they want the junk then let them buy it. But I certainly wouldn't provide it for them.
I get more nausea when I'm sicker, and foods I normally like will make be feel queasy. Pretty similar to having the flu, actually I'm not picky - usually I'll eat pretty much anything, unless I'm allergic to it. So I wouldn't be so sure that it's attributable to a mental disorder like ARFID. Typically when feeling like that, I want to avoid fatty foods and high-volume foods (most vegetables). Low-fat proteins and carbs (especially sweets) become my preference. Leftover foods can be problematic then as well, even if relatively low fat (a chicken leg), maybe due to congealed bits of fat being visible before it's re-heated.
It's something we definitely need to explore further. With the OCD issues and the fear coming into play, I've been reading about the four steps they often use for kids who are so afraid of eating certain foods, they'll actually starve before eating them. First step is making a list of the foods they'll be willing to try first. Then over time having them touch the foods......