I understand the point you're trying to make, but the analogy doesn't fit. My hypothetical child (or me) lying about where his faith lies is completely different than lying about who his father is. One of them could make a difference in the eternal perspective, one of them doesn't. Again, I think a more applicable story is Abraham and Isaac (of course it's from the Bible).
Let me put it this way...those terrorists have me, they say if I don't deny/renounce/speak ill of my faith that they'll kill me in front of my kid. If I do that, then isn't it possible my kid thinks that I don't think enough of my faith that it's worth dying for? Now would this be an easy decision? Of course not. However I would die for my faith, and I have no problem saying that. As a Christian, shouldn't we teach our families, friends and loved ones that death isn't a frightening result? If we truly believe, then we believe that when we die, we go to Heaven. There's nothing more glorious than that.
My kids know that my faith is immovable, and that it is the keystone to what I consider a satisfying life. I have no doubt that if I left my faith tomorrow and told my family how wrong it was, they'd still continue on without me. I don't doubt that for even a mili-second. So, no, I don't think that it is possible that my kids faith would be somehow diminished under the circumstances, especially considering that after the fact, I'd reassure her that I only said what I had to say in order to survive -- just like she should.
But go ahead and take a bullet for your faith. You'll be in Heaven, which will be amazingly awesome, and your family will be suffering like it was nobody's business down here for the rest of their lives. I don't understand that thinking, but, to each his own.