After careful observation, since you told me about the chain coming off, well I have a feeling that the item that's causing me my fits is the differential assembly.
It seems to be intermittent. I did some further trouble shooting by lowering the friction plate and turning the right wheel, thus making the sprockets turn freely,
sometimes the sprocket turn with the chain and sometimes not.
I wonder if there is a way to modify it?
After looking around for part replacement, they want $322. for the whole axle kit.
Once again, thanks for all your help!