The verse people use, and what it says

Protect yourselves and your families from a Fire. That verse gets produced to justify severity with children, so it is worth reading what it actually instructs.

The verb is protect. Not punish, not correct, not discipline. And look at the order in the verse. Yourselves first, and then your families. The parent is the first object of the instruction, not the enforcer of it.

That is not a modern reading arrived at to make the verse comfortable. al-Ghazali opens his chapter on the training of children with this same verse and takes it in the same direction. Our copy of the Ihya' 'ulum al-din holds it at section 26813. It is stored in Arabic only, so this is the sentence exactly as we hold it:

ومهما كان الأب يصونه عن نار الدنيا فبأن يصونه عن نار الآخرة أولى وصيانته بأن يؤدبه ويهذبه ويعلمه محاسن الأخلاق ويحفظه من القرناء السوء

The English beside it is our rendering and not a translation of record: since the father guards him from the fire of this world, guarding him from the fire of the next is more fitting, and guarding him is by disciplining him and refining him and teaching him beautiful character and protecting him from bad companions.

Notice what he says the guarding is made of. Teaching and company. Nothing else is in the sentence.