Yes the inclusion of children does change things, in that it makes choosing red even more obvious.

The problem is posed to the world. You have children, and they ask you what they should do. You tell them to pick red because you're their parent you can't bring yourself to have them risk their lives for some noble purpose.

According to blue buttoners, this parent is an evil person, right?

What if you entertain the variant of the question where a percentage of red votes die in the event of a blue win? It makes pressing red less advantageous, but also it totally changes the moral balance depending on the percentage.