I know that hindsight is 20/20, but I think I know two of your downfalls to puppy doom:
1) Puppies and 2 year olds- the worse mix on earth. Though amazingly adorable, the 2 should never exist in a house at the same time, at least not on purpose.
2) Dachshund. Did you research the breed first? I don't know much about pugs, but I know A LOT about dachshunds (I have 4 and had an older one that died a few years ago.
Dachshunds mellow with age. However, they require massive "teaching" and a constant eye when they are pups. They may be small, but as I like to call them, they are still crazed weasels. They are smart, quick, and simply insane as pups. They are lovable and will turn into a lap dog when older, but you have to keep on the training when young or they will eat your house.
I have a few helpful suggestions that you may have tried, but I'm throwing it out there anyway:
1) Gate off anything you can and put shoes behind the gate.
2) Crate train the weasel. It's as much for their good as yours.
3) This is a painful one- weasels are better if there are two of them. They tend to play with each other and leave the shoes as a second choice.
4) Put USA made raw hides everywhere, especially in the same area that you would find shoes. If the weasel has a shoe, trade it out with a chew toy and praise them with the chew toy.
5) Get pop can and throw a penny in each one. Tape the top. Shake it when the weasel is being bad. It's more effective then yelling, and the weasel will usually drop the shoe and run.
6) Did I mention crate training?????? Yeah, crate train.
Puppies are not easy, but the puppy time is short lived. The most insane weasels that I have had have turned into the sweetest, best dogs in the end. So, you just need to find a balance in your house and keep the weasel from eating the couch.
My first crazed weasel used to get under the couch, lay flat on his back and chew the underside of the couch. My second weasel liked to chew on electrical cords. My third weasel wouldn't sleep through the night and liked to chew on everything. My crazy weasel pair of 9 month old pups came from a rescue home. The rescuer gave them old shoes as play toys (yeah, that has worked out well). The three older weasels all outgrew their insanity and turned into total lapdogs. I'm still converting the younger weasels, though. They are a bit trickier because one is mellow but the other is a tazmanian devil in disguise.