Do you have her on a traditional leash and collar?Has she been to obedience classes ever?Is this a new behavior?
Can you explain her behavior when she's protecting you?Do you use a traditional leash and collar, or have you tried a Gentle Leader or Halti?
Does she bark and lunge at everyone?
It sounds like Sadie is the perfect example of a protective Schnauzer. Of course, having this makes walking her a bit of a challenge. There are a couple things we can try:First, if you think this behavior is due to some kind of anxiety, there are a couple over-the-counter products you could try to help take the edge off.
Melantonin is an over-the-counter drug that can be used to treat some anxiety issues in dogs. The dose you would give would be up to 3 mg given orally whenever necessary up to every 8 hours. More information can be found here: http://www.petplace.com/drug-library/melatonin-melatonex/page1.aspx , which includes risks, warning signs to watch out for and other bits of useful information.
Try a DAP collar. These are collars that are impregnated with a man-made version of the dog appeasing pheromone, which is a pheromone that nursing bitches give off to their pups to help them feel calm and secure. It's something that humans can't smell, but it has an amazing effect on dogs with anxiety and other issues. Although you can find them at your vet's office..you can also find them online at places like Amazon.com and Ebay for much cheaper. Just make sure they're DAP brand, as they seem to work better than some other versions.
Next, you may want to switch to a Gentle Leader or Halti rather than a traditional collar and leash. This is a training device that fits over the dog's nose and around her head. It is NOT a muzzle, but it does allow you to be able to control her head..and on a walk, if you control the head, you control the dog. This means that you'd have more control over how she reacts to people you meet. You can find more information about this here:
In addition to the Gentle Leader/Halti on the walk (which should be at least a mile a day to burn some of that misplaced energy)..you may want to consider buying her a doggy backpack to wear. It can carry your keys, water bottle, treats for her. It gives her a job (carrying it) and the extra weight will wear her out on the walk faster than she would without it. Working dogs such as Schnauzers will often work harder if they're doing SOMETHING...so using the backpack may give her something to focus on other than being naughty.
Finally, you should also get her involved in an obedience class. Not because you want her to learn to sit and stay (although this is great too), but because this will help her learn that you are the pack leader and that she should not act the way she does in public by elevating you to pack leader, it shows her that you're the one doing the protecting, so she doesn't have to..
I hope this helps.