Yes, the Russian troops were collecting their dead when a group of children escaped from a ground floor window. As the children were running away they were fired upon from the second story and the roof, and this is supposedly what forced the Russians to launch the uncoordinated attack as they couldn't just stand idly by and watch it happen.

The troops weren't planning to launch an assault (yet), and they wanted to have further negotiations (and probably better intelligence about the number, locations, and weapons of the hostage-takers before going in probably during nightime when they might have a better advantage).

How these murderers think that they'll actually get anyone to be sympathetic to their cause, I don't know. Killing children and unarmed men and women over unfeasible and unrealistic demands that still wouldn't lead to the safety of the hostages? Disgusting.