The most important thing to remember is that the burning of books can easily get the opposite results. In other words, it sends a message that there’s something that needs to be hidden, an idea or thought that should be kept out of reach. This tends to entice rather than repel. So then the next step is punishment or to pass laws to prohibit.
Your dad burned books as a way to send a message to his kids. Why not engage in conversation instead? Why not dispel or reveal the history behind and intentions of the author? If in fact my child was reading material that I felt uneasy with, the last thing I’d want is to drive them to read these books under the blankets with a flashlight.
The chances of small children reading any of the books you mentioned are pretty slim however. And if your teen or young adult children stumbled across Ayn Rand and are open about it then you have a golden opportunity to intervene intellectually.
Of course a parent banning books as a opposed to a government banning books isn’t the same but they come from the same place, a desire to limit the ideas that other people are exposed to. Ultimately, that’s not a good thing in my opinion. And it can turn really ugly quickly with dire consequences for society.