It's impossible to determine the internal condition of these hoses visually. However, this problem usually manifests itself through a failure of the brakes to release promptly, not in a failure of activation. In any event, the rear hoses would not flex in reaction to hard steering at very low speeds, so the back brakes should still be operative and provide at least a slight sensation of braking. Given the age of your car, I would replace them anyway, coupled with a flush of the brake lines.
However, I suspect that your real problem lies on the vacuum side of the system. I would suspect that the vacuum accumulator is not doing it's job, and that cutting the steering over hard at low rpm causes the power steering system to burden the engine, lowering the rpm further, and therefore, production of engine vacuum. The accumulator should be pitching in at this point to allow normal braking assist during this brief period. Apparently, it is not. In terms of vacuum, your brake servo is living hand-to-mouth, i.e., it is operating solely on whatever vacuum is being generated at any given moment by the engine. Review Desmondo's post.
I suggest a test: FIRST: Ensure that the parking brake is in good working order. Then, in an open, level, straight, deserted and safe area, drive up to about 20 mph, shift into Neutral, turn off the engine, and begin pumping the brakes. If you get 3-4 pumping actions before the pedal firms up, vacuum might be ok, if not, vacuum problem definitely. Just remember, you will lose power steering assist during this test as well, so be safe.