What you're describing sounds unusual. In an ideal situation, when you brake, even if you lock up the tires, you're going to continue moving in the same direction unless some outside force acts upon the car.
To spin a car 180 degrees requires a mechanical malfunction, or an outside force.
Start with the tires: are they the same on all 4 corners, and are they properly inflated? Different tires can have different properties, and having mis-matched tires can lead to unpredictable behavior. Tires with different inflation levels can also behave differently.
Next, check the brakes: are you sure that all 4 corners are working? You don't mention where you live, but if there's a fresh snowfall, go out to a parking lot or other empty, isolate spot and slam on the brakes from about 20 MPH. Without ABS, you should be able to lock up all 4 wheels - examine the skid marks and see if all 4 wheels locked up. If you have disc brakes, you can also check them to see if the surfaces are smooth - a rusty disc is an indication that the brake is not working.
Finally, check the suspension: bounce each corner of the car & listen for any noises and to make sure that the shocks are working properly (there should be one bounce, and then the motion should stop). Broken suspension can lead to spinouts - this, I learned the hard way :)
If you have any doubts at all, take it to a mechanic and have it inspected.
If there are no mechanical issues, then the problem is you: you're doing something that's upsetting the car. You can try to reproduce the situations in a safe environment to see (and understand) what's causing the situation so you can avoid repeating it.
You've had two close calls, and continuing to drive without understanding and correcting the problem puts yourself and others at risk.