Have you tried a head collar? The leading brands are Promise, Haltie, and Gentle Leader. They have a strap going around the dogs nose looking something like a muzzle. They work by pulling the dogs head around. No other way gives you such great control with so little force. The prong collar is now a dangerous relic of value only for its macho looks. Do not consider using one without hands on instruction from somebody with plenty of experience with them.
Technique may be more important than the type of collar. One gentle technique I
like is to just stop when he pulls. He wants to go. If you move forward when
the leash is slack, and stop when he pulls, he should quickly figure out the
only way to get to go, is not to pull. This is about teaching him not to
pull, not getting somewhere. The man that taught it to me said "If in a half
hour you haven't made it out to the front walk, fine, you have taught him a
lesson.'' A highly effective variation is to pull the dog backwards 5'-10''. Dachshunds have a reputation for being stubborn. The solution to that is an owner that is even more stubborn.
Another thing is leadership. I hope your class makes it a priority. Having the dog walk properly works together with other ways of claiming the position you must have. Dogs see all the people and dogs in the household as a pack with each having their own rank in the pack and a top dog. Life is much easier if the 2 legged pack members outrank the 4 legged ones. You can learn to play the role of top dog by reading some books or going to a good obedience class. A good obedience class or book is about you being top dog, not about rewarding standard commands with a treat. Start at
Raising Your Dog with the Monks of New Skete For more on being top dog, see
Establishing and Keeping Alpha Position, Letting your dog know you are the boss Here are some things meant for younger dogs like yours:
''Elevation for small puppies: Sit on the floor and gently put your hands around your pup's middle, below his front legs, and lift him up. He is facing you. Hold him for 15 seconds. Repeat until he no longer struggles. If he is past 10-12 weeks, lift his front feet off the ground, but don't pick him up.
Cradling for small puppies: Hold your puppy gently on his back, as you would cradle a small baby. If he struggles, hold him firmly until he quiets for 10-15 seconds. With larger pups, you can do this as your sit on the floor, with your pup between your legs.
Quiet lying down: Place your pup on the floor on his side, with all 4 legs pointing away from you. Use your hands on his neck/shoulder area and middle, to hold him in this position. When he is quiet, praise him. Lengthen the time that you keep him quietly in this position. When he accepts this position well, handle his paws and muzzle, while keeping him quiet.''
The quotes mean this isn't my original work. It is copied from my Puppy Raising Manual. I have long used these or minor variations of them, and they are very effective. You may want to give him a belly rub while he is on his back too. Helps bonding. There is a big difference between him rolling over and demanding a belly rub, and you choosing a time to roll him over and rub his belly. The latter cements your place as pack leader.