The Parable of the Flat Earther
Question Six: Although I do not believe in objective morality in the abstract, I certainly go through the day behaving as if there were moral and immoral actions, and I plan to impress my moral system onto my children. But then as a self-replicating communication-machine with no free will, I WOULD say that, wouldn’t I?
I do not get the joke. Your belief that objective morality does not exist in the abstract is contradicted by your behavior and your paternal duties to educate your children.
You are not acting like a man who, although knowing the world is round, still says ‘the sun rises’ even though both he and everyone who hears him knows the sun does not move from the center of the solar system. He is legitimately a man for whom the abstract knowledge of the shape of the world has no bearing on his daily life.
You are acting like a flat earther, a man too skeptical to believe the world is round, but if a flat earther were an airline pilot or an astronaut who crossed the International Dateline on a regular basis as part of his job. There is no logical way to avoid a contradiction between the knowledge of the International Dateline with the theory of a flat world.
So here. There is no logical way to avoid a contradiction between the knowledge of your paternal duty to raise your children with well-formed consciences with the theory that all the prompting of the conscience are meaningless.
If your moral system is correct, you have no duty, paternal or otherwise, and no reason to raise your children well, or even to raise them at all.