I'm sorry for the length of time it took me to respond. I typed up my answer and got thrown off the site and my answer disappeared.
Thank you for the reply. You are correct in that long term reasoning doesn't work in dog training. We must break things down into steps and give immediate positive or negative consequences. Keep training sessions short, when she isn't tired and make sure to use a treat that she finds irresistible (cat treats or dried liver, small hot dog chunks). We must make sure they know ultimately who is boss and who all good things come from.
Dogs are naturally pack animals. They rarely hurt their young when they are "training" their puppies in social behavior. There is a lot of facial expression, deep growls and vocalizations as well as shunning. Physical aggression is only used when all else fails and there is immediate danger to the pack or the pup themselves.
I personally don't believe in physical "punishment" in dog training. I think it makes them fearful rather than trusting and a dog that learns by fear is one that isn't reliably obedient. If they trust in you as the leader and that what you ask them to do is more
rewarding in the long, and short, run then they are more likely to comply. We need to be sure that the reward outweighs whatever negative behavior they are
about to do.
The nose is one of the most sensitive areas on a dog, and I would not hit a dog there. I have tapped a dogs nose with my finger when I had a treat in my hand to get their attention. It's a gentle tap along with saying their name and then I wave the treat under their nose to redirect.
It sounds like your wife is seen as a packmate rather then someone in charge. My old shepherd thought the same of my husband because he was a softie with her. So we need to change Dixie's perception of your wife. I would recommend that your wife be the one to take her to obedience class. All good, or lack thereof, must come from your wife. Walks, meals and treats should come from her and Dixie must follow a command to get whatever she wants, be it as simple as a pat. This program is called "nothing in life is free" and re-establishes who runs the show without a battle.
Here is a link to read about the program: http://k9deb.com/nilif.htm
The come command is the hardest one to train. I never give it unless I can reinforce it. So when I start working on the come command I use a long lead so I can reinforce the command. Make sure to reward profusely when she does come and use the long lead to guide her if need be.
Best of luck with your girl, your wife has some work to do but I think she and Dixie can come to an understanding.