The reason people say weightlifting stunts your growth is as follows
During adolescence, there's this thing in your bones or something, don't really know what it is, but anyway after adolescence, this thing fuses together with the bone, and you stop growing, which is usually around 18, in some people as late as 25. What happens is that if you damage this thing, you'll stunt your growth, but with good form/warm ups/stretching/not going heavier than you can handle, I assume the entire problem can be easily avoided. That's why most say wait till 18 to start lifting.
If you do heavy squats you will shrink a few centimeters but that is only gravity because your bones in your back are compacting but they will contract as you sleep. If you measure yourself as soon as you wake up and at night you will be a bit taller in the morning peace.
Heredity also plays a major role in height factor. If your parents are taller chances of you being taller is also High. But in your case as you are saying that your father is 5'4'' and you are 5'3'' and you want to increase your height up to 5'7''. I think it's possible as you ate in growing period, so you should consult a coach who can recommend you some special exercises and stretching activities to increase your vertical height. You must also consult a dietitian to help you with diets which are helpful for growth. And one more thing, don't try to lift very heavy weights because to some extent weightlifting affects vertical growth.