Fascinating thread.
I don't have children, but I'm on the other end of the spectrum - I'm the child.
I never knew, as a child, what kind of inheritance I would have gotten, had my parents passed away before I was 22. I think it was a yearly allowance type thing until after my education was completed, and then maybe a lump sum at 25? I'm not sure though. They never discussed it with me when I was a kid - none of my business. By the time I was 22, my parents decided to make my sister and I co-executors of their wills. Still, no idea what kind of money was involved, but we were made aware of where to find the proper documents if/when the time came.
Still to this day (I'm 31), I have no idea what the amount of money looks like, but I know it's probably north of a million or two. And that is with generous donations to charities every year. I don't know if they have donations to charities included in their wills, but I wouldn't be surprised if they did. My parents just retired, and I hope that they live long enough for not a penny to be left. Honestly.
I want their time, not their money.
And that last statement is important - because if it weren't true, they have made it very clear, over the course of my life, that I would get neither.
They raised me in a way that I don't need, nor do I want their money. And because of that... and ONLY because of that... they feel comfortable with passing it on to me and my sister.
Basically, my answer is: you know your child. If you trust that you've raised him/her to understand the value of a dollar, and make wise decisions if she/he were to come into this money, then you should feel comfortable passing the money along. If not, then it's your prerogative to do with it what you wish. Either way, that money is yours that you've earned, and whatever you do with it you should do with 100% certainty that it's the right decision.
My parents are my financial, and life, advisors. I talk to them about everything and anything. They know that the money they leave me, which will hopefully be in 30+ years, will go to my own children eventually. I don't factor a penny of it in my own personal calculations, nor do I ever intend to. It isn't mine. I haven't earned it. And if they change their wills later and decide that I get nothing, I will still have had the most amazing, thoughtful parents in the world. And that's the only thing that matters.