You’ve written that you don’t believe the Bible supports corporal punishment. What form of discipline do you think the Bible does support and what means of punishment are acceptable? And if you and, as you claim, the Bible, do not support corporal punishment then what do you do with a child who refuses a timeout? If you tell a child to sit in a chair or go to their room, and they tell you to drop dead, what is your response? Also would it not be safe to say that Jesus Himself used corporal punishment when he cleansed the Temple?
If your relationship with your children focuses on dominance and control like several of the currently popular “Christian” child raising methods espouse, then you have to accept the probability that sooner or later they’ll rebel. The more intelligent and spirited they are the sooner they’ll realize that your rules are arbitrary and your punishments are contrived, and they’ll call you on it.
The remedy is not to devise an “acceptable” form of punishment. The remedy is to change the nature of the relationship to one where such contrivances are no longer necessary. Some kids settle for negative attention from their parents because they can’t get any other kind, others rebel because the rules they’re subjected to are an insult to their intelligence. But there are no kids who come into the world determined to make life miserable for them and their parents. They learn to become rebellious from their experience with us.
By the way, using Jesus in the Temple is a wildly inappropriate comparison. Setting aside the fact that He’s God and we’re not, he was dealing with thieves and robbers and false teachers who were leading His people into Hell. They were also adults who were acting out of evil motives. There’s no evidence in Scripture that He ever treated children that way. Nor did He advocate us doing so.