Why does your dachshund terrier mix have breathing fits?

Could be Allergies. If you are referring to a something that sounds like a cross between coughing and choking it's probably what is referred to a 'reverse sneezing'. Mine do that when they drink water too fast, something to do with a flap in their throat. When it is bad, what I do, and works although it sounds weird, is wrap your hand around their snoot and blow air into their nose (don't blow at their nose, blow into it...not too hard though, it'll make them fart....just kidding, but really not too hard. Just a couple of short puffs seems to do the trick), it flips the flap back the right way.