Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear questioner, thanks for your important question, and we earnestly implore Allah to shower all those Muslims who died in that quake and tsunami with His all-embracing mercy, and may He Almighty grant all the bereaved tranquility and steadfastness.
First of all, we should not pass judgment on others, especially when we have not been tried with such a calamity ourselves. In an emergency we often act on instinct without time to reason. No doubt there are many survivors of this tragedy who are suffering from guilt because they were unable to rescue one or more loved ones, but they should not blame themselves for what was beyond their power. May Allah spare us all from such a trial.
In his response to your question, the prominent Muslim scholar Sheikh Muhammad Iqbal Nadvi, director and imam of Al-Falah Islamic Center, Oakville, Ontario, Canada, states:
This case has a number of fiqhi rules to stand on:
1. The safety of one's life takes precedence over others. One has to protect oneself first and then try to help others. So, if the mother can protect herself and her children, then it is her responsibility to do so. However, if she cannot, then her own protection comes first. This case is similar to the situation of delivering the baby when it would endanger the life of the mother, in which case we would save the mother and sacrifice the baby.
2. The rule of the lesser of two harms. If the mother cannot save the two children, then she can save one at least.
Moreover, the eminent Muslim scholar and renowned da`iyah Sheikh `Abdel Khaliq Hasan Ash-Shareef states:
There is no blame on this mother, as she was in a case of necessity as she could not rescue them both. We assume that she did her best to rescue them but could not; hence, she is not responsible for the death of one child. She did ijtihad (personal reasoning) and she will be rewarded for it even if she were wrong in her ijtihad. May Allah grant her patience and perseverance and bless her family.
You can also read:
Failed to Rescue My Wife in the Tidal Wave: Am I Responsible for Her Death?
Fate of Children Who Died in the Asian Quake and Tsunami
Helping Disaster Victims (Special Folder)