This is really strange. It sounds like she does have some sort of a physical problem. Did you explain the potty problem to the vet when he examined her? You may even want to get a second opinion from another vet.
The problem could be muscle tone. She may need more exercise and less food. Put out in the back yard by herself, she may just stand around or lay down. You may have to spend more time playing with her or talking a walk. Dogs need the stimulation of exercise to eliminate. A walk may replace the patting. You got a dog to enjoy spending time with her. She may require more time than you expected, but you took on the responsibility. Be careful punishing her, it may be she can't help what she is doing. Check her weight. Your dog definitely should be narrower at the waist than the hips and chest. As a Dachound ages, over weight, can lead to back problems. You should be able to easily feel the ribs, but not see them. Each dog is different. Standard recommendations are a good place to start, but each dog must have its food adjusted to its individual needs. See
http://www.purina.com/dogs/nutrition.asp?article=292. Finally go through the material below and see if there is anything you have missed doing.
Much of housebreaking is not training the puppy, but making it easier for your puppy, you, and your carpet while its body to catches up to its instincts. At around 8 weeks when the puppy goes to its new home, the time from when it realizes it has to go, and when it can't wait any longer is a matter of seconds. Only time will fix that. You can hardly be expected to be attentive enough to avoid all accidents There is no sense punishing the puppy for your inattention. It is not fair to punish you either, but you still have to clean it up if you didn't have the puppy outside in time.
Housebreaking starts before you get home with the new puppy. If you don't have a crate, buy one. I prefer the more enclosed, den like plastic ones. Skip the bedding. At first it gets wet, and later it can be chewed into choking hazards. A wire rack in the bottom will help keep the puppy up out of accidents at first. They are available with the crates, but a piece of closely spaced wire closet shelving from a home supply place is cheaper. If you already have a metal crate, covering it may help. Just make sure you use something the puppy can't pull in and chew. Dogs that start out in crates as little puppies, accept them very well. Never leave an unattended puppy loose in the house. If nobody can watch it, put it in the crate. I suggest letting the dog have its crate all its life.
Choose a command and spot you want it to use. The less accessible to strays, the less chance of serious disease. If it is a female, choosing a non grassy spot will avoid brown spots later. When you bring it home, take it to the spot and give it the command in a firm, but friendly voice. Keep repeating the command and let the puppy sniff around. If it does anything, praise it. Really let it know what a good dog it is and how much you love it, and maybe a treat. Note, being out there not only means you can praise it, but it also keeps it from being snatched by a hawk. If it doesn't go, take it inside and give it a drink and any meals scheduled. A young puppy will need to go out immediately afterward. Go to the spot and follow the above routine. Praising it if it goes is extremely important. If it doesn't go, take it back inside and put it in its crate and try again soon. Do not let it loose in the house until it does go..
At first it is your responsibility to know and take the puppy out when it needs to go. It needs to go out the first thing in the morning, after eating, drinking, and sleeping. If it quits playing, and starts running around sniffing, it is looking for a place to go. Take it out quickly. You will just have to be what I call puppy broke until it is a little older.
By the time most dogs are about 3 months old, they have figured out that if they go to the door and stand, you will let them out. The praise slowly shifts to going to the door. Some people hang a bell there for the dog to paw. If your dog doesn't figure this out, try praising it and putting it out if it even gets near the door. A stern "Bad dog!" is all the punishment that is effective, and only when you catch it in the act and are sure you didn't miss it going to the door. Clean up accidents promptly. I mostly keep the little puppies out of the carpeted rooms. Still I need the can of carpet foam sometimes. First blot up all the urine you can with a dry towel. Keep moving it and stepping on it until a fresh area stays dry. A couple big putty knives work well on bowel movements. Just slide one under it while holding it with the other. This gets it up with a minimum of pushing it down into the carpet. This works with even relatively soft ones, vomit, dirt from over turned house plants, or anything else from solids to thick liquids. Finish up with a good shot of carpet foam. Note, do not let the puppy lick up the carpet foam. Once the dog is reliably housebroken, your carpet may need a good steam cleaning.