I think you are dealing with two different issues. 1. Allergies 2. spoiled yorkie who has mom wrapped around his little paw
He knows now that if he doesn't eat "his food", mom may give him "her food". LOL It is hard to do, but best to put the food down and if he doesn't eat within a reasonable period of time, just pick it up and let him wait until the next meal. Usually they turn around quickly once they realize they are not running the show. Now, of course, you don't want him to go without food for days ... but usually they don't do that.
Now, of course, he could stop eating when he is itchy because that really is a miserable feeling. Just try not to give in and offer other foods.
I have an allergy pup. Sometimes she goes 6 - 8 weeks on the Cytopoint, sometimes a few months. I believe she has seasonal allergies.