If it's "shoes" that you have, one cause of the car turning to a side when the brakes are applied means that the other side may not be adjusted the same as the side it's turning to (makes sense?). Reset the shoes and make sure that the adjustment is even on both sides. After resetting, step on the brake pedal and recheck the adjustment.
Other causes could be a bad lining (maybe fluid soaked) different material on one side than the other, a hose blocked or internally bad, a bad wheel cylinder. All these should be checked out.
If the hoses are old, I would replace them.