That was the final straw. We initially decided to give the dog to someone else, anyone who didn't have other small pets or perhaps some farm setting with just big animals. There were no takers, so our next option was to either give her to the pound or put her down. I was not willing to confine the animal to a cage or cable run. After much thought, we came up with the following adjustment. It was sad to come to this point, but the dog simply can't be trusted around our small dogs.
Lizzie is now exiled for life, from being around her great friends and herd. She and Miss Cleo loved to play chase and other games plus generally ranged our large fenced yard of about 5 acres. My plan was to fence off a subsection of the five acres. That ended up being about 1/8 or 1/10 of an acre. Lizzie lives there during the day and the dachshunds have run of the yard. At night and when we are away on trips, Lizzie gets to roam the yard, but never at the same time as the dachshunds.
In the process of trying to solve this problem I also spent much more time training Lizzie. The other day when moving her from the pen to the open yard, our young pup named Callie bolted out the storm door and immediately attacked Lizzie, barking and biting at her hind quarters. I shouted for Lizzie to sit, and she immediately collapsed to the ground, paying the little dog almost no attention. Lizzie also does a great job of heeling now. Without a leash, I can tell her to heel and she stays to my left and behind me. She also will immediately go to her dog house when commanded. This extra control is very helpful and gives me added confidence in handling the dog.
Hopefully all of these adjustments will avoid the aggression problem in the future and also give Lizzie the best balance of freedom and safety than we can arrange. We continue to be sad over how this played out though, as Lizzie was raised with two small dachshunds from 8-10 weeks of age. We would never have thought that she would have this persistent trait.
Lizzie's exile pen:
So sorry you are having such issues with your much loved dog. It sounds like your training efforts are helping. IF all else fails and you are forced to find a new home for her try showing her at Pet Smart or Pet Co on Saturdays. You have the opportunity to interview prospective families and discuss her special needs. 
