Wa `alaykum As-Salamu waRahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear questioner, we would like to thank you for the great confidence you place in us, and we implore Allah Almighty to help us serve His cause and render our work for His Sake.
Answering your question, Sheikh Ahmad Kutty, a Senior Lecturer and an Islamic Scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
With regard to the hadith you mentioned in your question, it is best to translate the word idribuhum as spanking or even better as disciplining rather than hitting.
To infer from this that Islam allows corporal punishment as a method of teaching is repugnant to the spirit of the Sunnah as we can safely establish from a close study of the Seerah and the Prophetic traditions.
As we learn from his beloved wife `A’ishah, the Prophet (peace be upon him) never hit anyone: neither a man or woman, young or old.” (Ibn Hibban and At-Tabarani)
Anas (may Allah be pleased with him) who accompanied the Prophet (peace be upon him) from the age of ten said, “I served the Messenger of Allah for ten years and yet during the entire course of time not even once he condemned me for any mistake I made!” (At-Tirmidhi and others)
In other words, his method of mentoring was by setting examples, practice, and character.
It is for this reason that Allah orders us to emulate his beautiful examples.
Allah Almighty knows best.