Alot of factors here but first off, a non ABS car will lock up the tires if the brakes are slammed unlike ABS which will pulse (releasing and applying the brakes incrementally). That said, in your case I am not sure what you are expecting or what the car is actually doing. If the brakes are locking up and the tires are sliding, thats what an old school brake system will do. Ideally the front lock before the rear, but they will all lock nonetheless.
Have you changed the entire brake system (MC, proportioning valve, metering valve, etc.)?