No one knowing you and mim could think you were bad parents. You're great parents both of you, and you're a loving, intelligent father.
Like zombie-monkey, I got spanked from time to time - mostly I really deserved it, once or twice my parents lost their tempers. In no way would I consider either to be abusive - kids sometimes won't listen to explanations or arguments or reason. They often want what they want, right now - even if that's running into traffic. A short sharp spanking gets their attention and makes sure they don't do it again in a hurry. Afterwards - it's good to be reminded that someone can be angry with you and still love you. Or you them.
Sounds like he's no loss off your reading list.