I honestly can't tell you if I would really go through with it because I'm not a parent. I do know that parents develop a deep bond with their children and it's also instinct for many mammals to be protective of their young even if it endangers them.
Seconded... sort of.
If I was just given two children to call my own, and then placed in this situation, I'd probably do something similar to Sophie and save the 'weaker' one, so to speak. Even if the option to give one's own life up was on the table, I'm not sure the love I presumably have for these children would overcome my fear of death. But that's my personal fears overcoming the moral conundrum.
However, pretty much no parent I know would do this, given the same situation. On the multiple occasions when I was younger that I'd put my parents in hypothetical situations like this over who they'd save over me or my brother, they've always said they'd give up their own lives before having to choose. All of my other friends' parents - or friends who are parents - would undoubtedly say the same.
And yet, none of them have actually been placed in a situation like this. It's all very well 'saying' that you'd do something, but when push comes to shove... I honestly don't know how many would make the ultimate sacrifice. At this stage in my life, I probably wouldn't, unfortunately...