Too bad you can't post pics. His problem does have a name it's called "Submissive Urination". Do a search on Google and you will come up with lots of info to help you through this. Also the good news is he may grow out of it, but you are wise to not want to wait just in case he doesn't...... One of my Doxie's had this problem and it took lots of time and patience to get her over it, so there is hope. Rather than me tell you how to do it I think it might be better if you were to read about it.
Here's a link that has many of the sites that I think will be helpful to you. http://www.dog-play.com/peeing.html
Another good link http://www.geocities.com/Petsburgh/7742/training/submissive.htm
Not much going on the DORG board, you might want to join a couple of Dachshund Websites if you have any more questions.
Keep working with your pup I know you will be able to correct this behavior. Good luck!