Hi RMo2:
I don't have the same issue with my girls, however, I agree about keeping the dog food away from the chicken. I know the dogs would find it most inconvenient to not have it out to graze on, but perhaps you'd consider just having set meal times for them instead, even if it's just a temporary thing. It doesn't have to be a firm 6am & 6pm kind of a thing, but just whenever breakfast and dinner times work for you & your schedule.
As far as soft but nutritious foods go, why not feed her scrambled eggs? Mine go CRAZY for them, especially when I mix in a little fresh garlic. If she likes them, that could help her nutrition intake and with weight gain. I've also found that getting some white fish fillets from the store on occasion (cod, tilapia, whatever) & cooking them up in a skillet (just poaching with garlic, not frying with oil or breadcrumbs) is a nice treat. And my girls love tofu, as well. I get the organic extra firm, drain the liquid, cut off a portion, leave the rest in it's container & pop it into a ziploc in the fridge. I mash the tofu with a fork into small bits, add a mix of chia seeds, flax seeds & sesame seeds, stir it up & watch them go to town. There is a lot of protein in the above "treats", but they also have their regular food. It may just be my girls, but I found that eggshells didn't provide enough calcium for them. I give oyster shell & they take what they want/need. Same with grit. Even though your girl is on a soft diet, grit would probably be a good idea.
In any of the above, I don't see why you couldn't "trick" her into eating her own food by sprinkling some into the eggs, fish and/or tofu. I'm assuming that you (are trying) to get her to eat mash & not layer pellets. Regardless, if she gets a taste for something other than her food, it might be difficult to get her to eat later. That's why I'd sprinkle some into the above, just to make sure that she's familiar (& reacquainted) with the taste of her own food. You can adjust the proportions later.
I hope your chicken baby is well on her way to being healthy enough to rejoin her flock! You're a good Chicken Mom to let her stay inside while you tend her. Way to go!