Demodectic fussy eater with gastric problem

Hi,
I messaged this to two member of this forum, but i want to post it here also, in case someone else also have suggestions.
And I am actually torn between posting this in Food section or Health section, but since I'm asking about how to feed, so I post this here.

So, I have a 1yr old female Shih Tzu puppy. I've had her since she was 3months old, but she was not very healthy. Turns out she is demodectic and have gastric problem. So she's becoming a fussy eater since I am terrified of her getting sicker if she does not eat.

I have tried numerous dog food mixed with pedigree sachet (she won't eat cesar or other wet food), tomato, peanut butter, and these last months I'm using Plain Yogurt. I haven't tried cooking for her, that is because i want to keep her face clean. When i gave her steamed mince meat, she learn to only eat the meat, and been doing that ever since. I really want her to eat dry kibble only, its cleaner and thinks that it would be better for her teeth.

I feed her twice a day on schedule, but she really is controlling me, if she thinks the yogurt is not enough, she would sit back and bark at me to add more. If I ignore her, she would go to sleep till I take away her food (she don't care if i took her food away). Sometimes she prefer to sleep than eat, so i have to really shake her up (she's a heavy sleeper).

Since reading your reply, I realize that I am truly making a monster. But problem is, I had tried strict schedule tough love system, but since my puppy is demodectic, if she's stress or weak, she would have hot spots. Plus with the gastric problem, if she don't eat for like more than a day, most likely she will vomit.

I have tried putting her food down and walk away, then took it 30 minutes later, but she totally don't care. And last time I tried it, she didn't eat 3 meals time and ended up vomiting yellow liquid. I assume it was gastric acid. So I went back to the yogurt mixed kibble.

How long do you think I can ignore her for not eating? If she vomit, do you think it's alright. My vet (said by most people) is the best in town, and she said that if she don't eat for 1 day, she have to have infusion and that i should "look for more food"

I have done a lot of researching, but i haven't found a demodectic, gastric problem, fussy eater.
Oh, btw, i have another puppy, and she also don't care if the other puppy eats her food too (she's just so ignorant, i don't know what to do with her)

So, I hope anyone have some suggestion, any suggestion, for me.
Thanks a lot in advance.

V & Baby