Hi I am not a professional dog trainer. I am just suggesting what I did with my girl.
What I am doing is working off leash in my house with a treat in my hand. I will start by just taking a few steps then gradually add up to ten steps.
The reason why I did this is A) I read it somewhere! But the best reason is because I found myself stopping and turning so much that I was dizzy. LOL!
Anyways I was just pulling her so much that what I found is that her natural response was to pull back.
An example was if someone pulled on your arm, your first response would be to pull back. So I learned that because I am not a professional, I was not doing it correctly so I was doing unintentional training.
Just another idea maybe
This is precisely what I was going to recommend.
You've got a long history, with both this dog and previous dogs, of leash battles, right?
So, throw away the leash for the heeling exercises. Get rid of it.
The more you depend on a leash and some certain type of collar, the less you'll ever be able to do without it.
True obedience comes with the dog working at liberty.
Make it a very controlled setting, safe, and with as few distractions as possible, and learn to click/treat her for every step that is even approximating the appropriate, mannerly position.
Be careful using lures too much. Your dog's behavior may become dependent on a food lure, if you use it incorrectly.
The general rule is to lure once or twice on each new behavior, no more than three times, then phase out the lure.
That does not mean you get rid of rewards--you're just not showing them to the dog--you present them after the dog gives you the asked-for behavior.
There's really no way to explain all this over the 'net.
Get the CU book, and the accompanying DVDs and really, really try to get into a better class. Correcting this dog in the manner you've described your instructor is trying to do will make her worse, not better.
If your choices are that, or Petco, go to Petco. At least you can do your own thing there in a non-harmful way, with a group of dogs for distraction--BUT you need to get the basics down alone before you go, esp. since she is reactive. Try to get some private lessons, if you can also, first.
As far as your link, it looks worthy of further investigation.
I wish her site was a bit more informative as to her credentials and philosophy, but since she offers Clicks for Tricks, and does agility training, it looks like she might be a resource for you to learn basics of operant conditioning (clicker training).