If you genuinely attached infinite utility to your family's lives, then we could remove the finite terms in your utility function without affecting it's output. You are not valuing their lives above all else (...)

You do have a point, but there is another explanation to resolve that, see this comment.

We still have a fundamental disagreement on whether rationality is in any way involved when reflecting on your terminal values. I claim that rationality will help the closet murderer who is firm in valuing pain and suffering the same as the altruist, the paperclipper or the FAI. It helps us in pursuing our goals, not in setting the axioms of our value systems (the terminal values).

There is no aspect of Bayes or any reasoning mechanism that tells you whether to value happy humans or dead humans. Reasoning helps you in better achieving your goals, nefarious or angelic as they may be.