The LA Doxie group can be found at
http://pets.groups.yahoo.com/group/LADOXIES/It is a very diverse group who in common share a love for their dachshunds. We meet at dog parks the 3rd Sunday of each month and occasionally have impromptu meet ups. One meetup is a hike, one a holiday party and at least one in the summer is at a dog beach.
One if the members, Joy Brun runs a rescue. Her website is:
http://www.doxykeeper.net/She is in Lancaster but places dogs all over.
Dena Delgado heads a larger rescue, Southern Ca Dachshund Rescue:
http://www.delgadog.com/She places many dogs and has several dogs being fostered in the valley. Her organization also hosts two really fun fundraisers each year: a Hallowiener Picnic and the Wild West Wiener Roundup.
Either one of these ladies can help match your family and current dog with another dog to adopt. There are fees for rescue dogs because these organizations spend a lot of money vetting these dogs and caring for them so they are healthy enough to go to new homes.
Best of luck and let us know what you end up doing.
Suzee