Woo... where to start?
First off - I don't know what it means to look at a puppy and decide it's a "dominant dog." I'm wondering if whoever told you that might have set you up for some initial troubles - other than the obedience classes, did you do anything differently with your puppy because she was "dominant"?
Teadrinker:But then, suddenly, at the age of 2, she started lunging at innocent passer-by once in a while
This is actually relatively common and relatively easy to fix. My dog did the exact same thing, and I never figured out what it was that "set him off."
Teadrinker: We sharply reprimanded her every time she lunged at people, thinking we were correcting her.
In my opinion (others may disagree) this was the wrong thing to do. It's a logical thing to do, thinking as a human, but from a dog's point of view it can actually cause the unwanted behaviors to escalate, as it seems it might have with you. The dog is walking along and sees someone scary/threatening and starts to lunge and growl to fend off the offensive person. By "correcting" the dog at that time, you can add to the dog's belief that the offensive person really is offensive - after all, all the dog is trying to do is defend herself and chase this person away and the dog gets yelled at! The offensive person causes the dog to get yelled at! But after the dog lunges and growls, the offending person leaves, so despite the yelling the dog was victorious.
In my opinion, the best course of action for such troubles is positive reinforcement of appropriate behavior (being calm and quiet), systematic desensitization (so the dog associates passing people on the street with good things happening), and redirection of attention (paying attention to the person holding the leash instead of the passer-bys). There are a couple of books that are really helpful with that sort of system, including "Click to Calm" and "The Cautious Canine."
Teadrinker: But then.. the last day of the summer (we usually go away), she bit someone. And the next morning, bit someone else. Both times she was in the care of an employee.. he'd been irresponsible in both cases by not having the dogs on a leash. The first night, he'd brought them to a dog park, and had returned to our home with the dogs seated in an open Jeep Wrangler. He opened the car's door's thinking the dogs would run into the house, but instead, both dogs charged at a man and woman strolling by.. and they barked and barked aggressively, he said, for like, 3 min., with the man holding up his arms to the dogs and the lady cowering behind him in fear. The employee kept calling the dogs but they didn't listen, and then our dog went around and bit the lady in the buttocks. The next morning, this employee came over to bring the dogs to the dog park again.. opened the door leading to the garage thinking our car was in the garage.. but it wasn't, and worse, the garage door was opened to the street, and a woman was walking by. Same scenario.... both dogs charged out (again unleashed) (this employee was fired by the way), and again our dog bit this other woman in the buttocks.
I don't really understand what you wrote here... was this like a dog daycare/kennel sort of place? If so, as you noted, the employee was highly irresponsible. Guarding the house is a very typical behavior and most dogs will do it to some degree or another - it's very likely that the dogs felt they were defending their home from intruders, not so much that they were just biting people for the heck of it.
Teadrinker: I've spent thousands of dollars on trainers since she was a puppy.
Could you share with us some of the things the trainers have said? What did they tell you, what did you do, how did it work? How long did you follow their directions, if they gave any? Was everyone in the house working on the training in the same way?
Teadrinker: This time, I was away, and my husband walked the dogs. A lady passed by, and Tif passed in front of my husband and jumped up and (I guess) bit the woman.
Again, this scenario confuses me. Was the woman passing very close by? How was Tif able to jump up and bite the woman while your husband was walking her - what was he doing? Was she on leash?
Teadrinker: When I heard this, I knew we definitely have a problem dog. I just read CESAR MILLAN's book and it was excellent. I now know that she is a domiant dog in dire need of a leader. Our household is too busy and too many people are responsible for our dog's care.. and because of that, there is not a solid leader in the house, so she is the leader, and she feels she must protect.
Now there are lots of people on this board who will disagree with me, but IMO reading a book or watching a show by Cesar Millan can be a classic example of a little bit of knowledge being a dangerous thing. IMO Cesar has a great deal of success because he has a great deal of experience working with dogs - for a lay person to attempt to imitate his methods or diagnose their dog's problems based on his work can lead to some serious problems. IMO.
I do think you're right in recognizing that your dog needs some leadership, however. I do not think this is a "dominant" dog or a "need for dominance" - it sounds like for one reason or another she picked up some bad habits that she never quite got over. I'm totally guessing here, but maybe there hasn't been a lot of consistency in her training? It sounds like this dog would benefit greatly from some "Nothing In Life Is Free" training (http://www.k9deb.com/nilif.htm), but for it to be truly effective everyone in the household has to participate in the work. If one person is asking the dog to sit before she's allowed inside, for example, it completely negates the effect if other people in the house let her come in whenever she wants. That means no lazy bums, even the kids have to work! 
One really important fact you neglected to mention in your posts - when you say your dog is "biting" people, how hard? Is it a nip, or is she bruising and/or breaking skin? Also, how old was your dog when you got her?
From what you've said so far, it sounds like she has some really basic and (relatively) easily dealt with issues. My dog has had some very similar behaviors, but after a lot of work and a lot of consistency he's given up most of them. It sounds like your dog is wary of strangers and perhaps exhibiting some "preemptive aggression" ("I'm going to get you before you get me!") and that carries over into walks, new people entering the house, and strangers passing by the house.
I also would recommend a vet check and a full blood panel - I know a lot of people on this board have had "aggressive" dogs that turned out to simply have a thyroid problem. With the appropriate medication they "recovered" completely.
I would be happy to share a more detailed description of what's worked for me and my little stinker dog if you think it would be helpful. I'm primarily curious/concerned about how hard your dog has bitten and what other types of training you have tried - those two answers will really define what course of action might be best.