I read Ian Dunbar's "Before and After Getting Your Puppy" before I brought my yorkie home. He is big on kong training. A kong for your size dog is under $10. I bought several for my pup. It took a while to teach her to use them. At first, you put the highest value treats in them and don't pack them tightly. Once they get the hang of them and figure out how to get the food out of them, you can pack them tighter and mix up the ingredients, just putting the highest value treat in the bottom, a little in the middle, and a little at the opening.
They are a dog owner's best friend, used correctly. If your dog eats kibble or mostly kibble, you can teach your dog to use the kong and they can eat ALL of their food from a kong - it keeps them busy and they don't have time to be bored.
Sounds like your pup is in charge, and that has to change - but won't without help. You'll need a trainer good with positive reinforcement to switch things around. Meanwhile, try introducing the kong. Both your dogs can enjoy them. They even make a small one in black (heavy chewer) now.
BTW, I bought a small dog shock collar for our poodle boy years ago. It has 9 settings and is supposedly "humane and safe". I put it on my wrist, put in on the lowest setting, and hit the button. It's still in my garage, collecting dust. I wouldn't do anything to my dogs that I wouldn't do to myself - and no dog in this house will ever wear one of those. I have a high pain threshold and that was awful on my WRIST. Cannot imagine it around your NECK.