how hard it shift depend on how hard I step on the gas petal, or how high the engine rpm is.

I try to avoid this by turning slow, and not to step on the gas petal.

 

The only things that may change when turning really are the CV axles and the differential. Other than those things I can't think of many other things..

Unless turning has no effect on shifting which you're saying it does.

 

Moparkyle,
Before, I kept thinking it's the transmission that caused the car to shift hard like that, because that happened when it shifted gears.
Thanks to you, now I think again. I think it's very possible the differential caused that to happen.

I will do more research on the differential to know for sure.
We haven't changed the fluid for the differential since we bought the car at 30,000 miles on the odometer reader. The car is now read 70,000-75,000 miles. The previous owner probably didn't change the fluid for it either. On the manual book, it suggest to change differential fluid every 30,000 or 45,000 miles if I remember.
I will change the fluid for the differential when I have times. Hopefully that will fix it. If not, it could be the gears in there.

Thank you all for your helps.
If you have other suggestions, please let me know.