Also, how was the relation between a cesar and his kings in general?
The quote what Caesar Augustus said is actually "It is better to be a pig at Herodes' court, than one of his sons". King Herodes was an ally of the Romans for a long time, and was generally supportive of Roman leadership. Foreign kings were often well known by the Roman emperors, for controlling them was an important part of the stability of the Roman empire. The empire, especially in the early days, consisted of a lot of client states. Basically kingdoms or tribes or whatever nominally free and an ally of Rome with their own kings, but under Roman rule.
King Herodes was quite violent in his rule, often striking hard and without mercy at rioters. He also was know as a paranoid man and made many of his family members (and three sons of him) stand trial for so called conspiracies against his rule.