Hello Beta:
Jakir gives a good answer.
I might add that first, we address "Brat" which is a child with a "fighting" attitude, who will not obey or listen to others.
The adjective "rotten" merely advances the idea that a child who is at the very least, a bad child, or "brat" is even far worse. "Rotten" means that something inside is seriously wrong with that child, such that the disobey all the time.
Associated with this is the concept of the "Spoiled" child, which is one whose parents have given the child absolutely everything he or she wanted, and never made them obey or show respect for rules.---Warm Regards, Bruce