Shoot, Jim.....I've been in and out of airports and reading this on a friggin "smaht phone" so this thing lost me at Cliff's first post!
Now that I've gone back through some of it (certainly not all of it) Justin makes the most sense by far (great post Justin!), but I'll add just this:
Yes - under severe braking, the car, en toto, will try to follow the front wheel trajectory if they haven't locked up.
However!
You must remember that these cars only have rudimentary rear brake adjusters that most-of-the-time get rusted or gummed up and don't "adjust" even remotely as they should.
The chances are, with a drum brake rear that neither of those drums have been adjusted perfectly to the characteristics of the front wheels, nor are they perfectly adjusted side-to-side, so THAT means that when applying the brakes, one rear wheel will engage first and harder, given the same pedal pressure, and THAT will cause a pull to that side and will try to come around first in that direction. This is totally unrelated to what happens when applying the emergency brake.
For example, back when I was still lazy about it, applying the brake pedal on my speedster would make my car pull slightly to the right> because the right rear drum was adjusted very slightly tighter than the left. Harder application of the pedal made it pull even harder to the right.
If I were to pull on the handbrake instead, the car would try to pull to the <LEFT because that side's cable was adjusted slightly tighter than the right. It consistently pulled to the left until I adjusted the e-brake cables to even things out (tested on a long, straight stretch of back road and confirmed in a relatively level parking lot).
So there is a balancing effort required between the front and rear brakes, and then between both sides in the rear as actuated by the pedal to balance left-and-right, and again between both sides at the rear to balance the hand brake. They are totally different braking systems.
Get all of those things balanced and the car will stop sort-of straight, forgetting all of the effects of different tire adhesions, pavement irregularities, humidity, where the front wheels are pointed and all of that other stuff.
The bottom line is; Cliff should take it to his mechanic, not give them ANY of the stuff presented in this thread and ask them to check out the brakes, adjust the rears and balance them left-to-right via a set of panic-stop tests (there is no in-shop test to do this...It must be done as a road test), then do the same for the hand brake with another set of panic stop tests. Any decent "older car" mechanic knows that this is the ONLY way to test drum brakes for balance and that it is a trial-and-error process. Get all that done and it might still try to swap ends in a panic stop because of pavement irregularities or operator moves or whatever - you just don't know.
Geez....You guys typed a whole LOT while I was away!