Well...It depends what training methods you use, it's hard to recommend one as everyone believes whatever way they train their dog(s) is the best way in the world, and on such a forum it's a good way to start a war lol I tend to follow Cesar Millan's training methods for the most part.
As far as your older dog, they all have their own personality. I've found dachshund in general despise me for some reason. Maybe it's my height, I dont know but to me, any way, they've always been aggressive towards me and my dogs. It could be in the breeds nature.
I think letting your older dog sniff the puppy was a good idea. Do they have crates to sleep in at night? If they do, what I would do is put the crates next to each other (not side by side though) and put your older dog in his crate first, close the door, and then put your puppy in its crate and close the door. This puts the puppy in the older dogs "territory" for long periods at a time safely.
I think showing your dog it's in the wrong is also a good idea, but again, it depends on your training preference. Swatting on the rear end may not work because it's not a natural behavior for dogs, it may not understand why you did that or what you wanted to obtain from doing that. I found if my dog is on the couch or the bed and misbehaves I make it get off and lay on the floor, kinda like saying "you don't behave this way here."
I've seen people making the older or more aggressive dogs submit to the younger or calmer ones. People do this by making the older/aggressive dog lay down on it's side in front of the other dog, or taking your older/aggressive dog and turning him so his back end is facing the other dog - this lets the other dog smell him and takes the control away from the older/aggressive dog. To me, the older/aggressive ones want to run the show, they want to be the boss, they want to conduct meetings and interactions their way lol which for some means no meetings or social interactions what so ever, it just means you and them, no people - friends or family - no other animals - cats, dogs, nothing. They want to have the last and final say, no questions asked.
I've also seen people achieve these things with clicker training. I dont know how, but it's a way to look into.
That's about as much knowledge I have, personally, on the subject. My recommendation would be to take them both to a training class, talk to a dog trainer or behaviorist. There are a lot of How To Train Your Dog books out there, Cesar Millan has a few I like and use. Read up on different training methods like the clicker training.
Sorry, I realize that isn't an immediate answer on what to do.
