Can one teach Objectivism to one's parents?

My personal opinion is that it depends strongly on the relationship between you and your parents. For the vast majority of cases, the relationship is such that you are unlikely to be able to fundamentally change your parents' world-view, and if their world view is incompatible with Objectivism, you are therefore unlikely to be able to change it. However, I think it is certainly possible that if your parents became interested in Objectivism on their own (i.e., changed their own world-view), then you could teach them the concretes of what Ayn Rand actually had to say in various subjects.

There are a very small number of parent-child relationships I've observed in which a child could potentially alter their parents' world-view, and nearly all of these involve a parent who is either particularly lacking in confidence or particularly intellectually honest.

I'm not aware of any cases in which a child has successfully taught their parent Objectivism.

I take "teach Objectivism to one's parents," here, to mean help them understand and accept the philosophy. I have tried to do this for both of my biological parents, so I have some experience with this issue.

My father is like an Objectivist in many ways. He's rational; he's intellectual; he rejects religion; he's goal-oriented; he strives for personal success; etc. On the other hand, my mother believes in God, but she's honest, committed to her values, and religion does not play a large role in her life. When I tried to present Objectivism to them as a philosophy (separately), neither were persuaded. They weren't upset, but they weren't interested in being converted by me. Perhaps this is what Ayn Rand and Leonard Peikoff are referring to.

However, I have had some success, not by lecturing my parents, but by gaining their intellectual respect and offering ideas with my philosophy implicit. With this approach, they don't need to view me as a teacher; there is no "ideological pill" for them to swallow; they only need to judge the ideas, which is something any honest person can do.

For example, when I was younger, and my mother had made a decision, she would often refuse to hear what I had to say. But now she respects me intellectually (because I'm intelligent, offer good ideas in general, do well in school, etc.), and so she often comes to me for my thoughts or for advice. This advice contains implicit philosophy, so when she accepts it, I'm to that extent teaching her. In this sense, I have taught her about the importance of being first-handed, rational, speaking and writing grammatically, etc.

Sometimes our conversations do become explicitly philosophical. After we had a discussion about religion, I haven't seen any evidence that religion plays any role in her life. I think she was afraid to offend God by questioning his existence, but I made her feel more comfortable about doing so: A benevolent God would not damn someone for doing their best to understand.

As for my father, he appreciates my insight, but we already have so much common ground. In fact, because he's more experienced with the world and has a generally rational perspective, I still learn a great deal from him.