My daughter tells me I have the worst predators living in my house - two miniature dachshunds. Have you had any problems with your dachshunds and the chickens? Of course my dream is that everybody lives together peacefully, but I know I have to be realistic and aware they have been bred to be little hunters.
I bet she is right. Dachshunds were bred to chase rabbits through thick brush/thicket. I really doubt you can take the hunter genetics out of the dog. Just like chicks know what to do immediately after they hatch with no help. You might be able to train them to ignore the chickens when the chickens are full grown but I suspect a little chick dashing off when spooked (which my 4 week olds seem to do for no reason at all!) would trigger a chase without so much as a microsecond of thought and those little mini dachshund legs are FAST. Instinct doesn't require thought and isn't controlled by it, at least not at microsecond number 1.