I'm generally a consequentialist (I think I spelled that wrong), so in my opinion, what is morally good depends on the results each choice will yield. So in the first situation, I would probably choose the girl to die, because the boy would be morel likely to survive working in the labour camps.
In the second, and this may sound a little weird, but I would tell my kid how much I loved him/her, then I would kick out the chair... because I would possibly feel even worse if i just stood there while another person killed my child, than if I were to do it as tenderly as possible. Then I would wait until the executioner was alone, and I would kill him for making me do that to my child. Not really consequentialist, but a cock deserves it I think.
On the ship, I would ask for volunteers to leave the ship, then I would select the 'weaker' people, for the lack of a better word - so the old, the sick. And the fat people would have to go, because some of them weigh twice as much as the average person and therefore I am saving more people by throwing them off first.
those would be my 'solutions', not perfect, but reasonable I think.