Paul,
If you got the Dachshund from a "rescue group" and not the animal shelter, sounds like the problem is with the rescue group. They didn't keep the dog with a foster longer enough and test it under various conditions to make sure it was compatible with your type household. It may very well have been that dog needed to be put down..... sad as that may sound.
We've adopted two racing greyhounds from the National Greyhound Rescue. The husband & wife team that runs the local chapter is VERY thorough in their foster program and screening of the people who plan to adopt.
If you got it from the shelter..... well, most people that work these places mean well, but don't know dogs like they think they know dogs. We've also adopted mixed-breeds from the shelters and had very good experiences. But then my wife and I are familiar enough with most all breeds ( more so my wife) and we have a pretty good idea of what to expect from the breeds involved in our mutt of choice.
It's really a farce that mixed-breeds are healthier than purebreds. It just seems that way because most people aren't going to spend hundreds of dollars to care for a dog they paid $40, $50, or $60 for. You hear about the purebreds because breeders invest in their dogs..... which equates to more vet care in hopes of preventing or escalating further health problems. For example, it's a fact that all large breeds are susceptible to hip displaysia. Just because you mix a collie and a rottie doesn't mean you're not going to have to deal with hip displaysia at some time in that dog's life.
But to get back to the root of your question..... If you get your dog from the shelter (pound), ask to take the dog off to an area away from other dogs, cats, and distractions. Spend some time with it to see how it reacts to you; if it's not interested in you or stand-offish, it's probably not the dog for you. And if you have kids, take them with you, but be cautious. A dog may be fine with adults, but hate kids. You'd want to find out if "poopsie" would rather eat your children than play with them, in a controlled environment before you find out at home.
If you're going to get it from a "rescue group"... ... do the same, but ask about whether it has been tested for whatever scenarios that are particular to your home. Not every scenario is going to be tested for, but at least you'll have a better idea of the dog's background. For us, cat testing was a must; we sure didn't want a greyhound that would rather hunt down our cats than live with them.
Just food for thought.