"Spare the stick and spoil the child"

That proverb is misapplied. When you look at the original Hebrew in context the stick was a guiding stick not a beating stick. A guiding stick is one used for gentle nudges to keep someone on the right path. Basically the proverb is saying: An unguided child is a spoiled child.

Today is is often interpreted: An unbeaten child is a spoiled child. However, this is not the original intent of the passage at all!

I don't have a biblical commentary on me but if you want to check I suggest the Anchor Bible series which generally provide high quality modern scholarship with extensive bibliographies.