Public or private?
Don’t be so indiscreet as to spank your children in public—including the church restroom. I get letters regularly telling of trouble with in-laws who threaten to report them to the authorities. Parents have called the Gestapo on their married children. Church friends who have noses longer than the pews on which they perch can cause a world of trouble. If you cannot get them trained before going out in public, stay home and read our four books again.
As to whether or not you should discipline your children in front of the other members of the family or in front of close, trusted friends, that is a matter of choice. In our home it did not make any difference to anyone whether the other family members were present. The children receiving the discipline were occupied with much more pressing matters.
When the rod is being used as training, it would be totally counterproductive to remove the child from the scene. For the rod to be effective as a training tool it is best delivered within seconds of the offense. If it can be delivered immediately, that is best. If a child is trying to stand up in his highchair and he receives a swat every time he puts his foot under him, he will be trained quickly. If you took him out of the highchair and removed him to another room, you would not be training him to stay in the chair. Parents who hold fast to the philosophy that you must remove the child to a private place are unable to train. By the very nature of it they put off spanking until the situation becomes unbearable. They fail for want of immediacy and therefore, consistency.
Respected and Wholly Loved Children 
I’m of the opinion that “the Gestapo” needs to be called more often in these cases. But it’s very hard for fellow Christians to step in, especially if they look at the situation and think, “There but for the grace go I and my family.” Child-rearing has become such an “each family chooses for themselves, don’t interfere” situation, that most Christians will just look the other way.
There needs to be better explanation and exegesis–from the pulpit, in Sunday School classes, in Bible studies–on just what that “rod” is, and what those verses mean in the original tongues, instead of taking the English version as the final word.