Well you never ever see a child get harmed in a mainstream video game, so this is a first.
I think its bad but not as bad as no Russian. That is like now one of the most infamous levels ever.
I think its rather cheap however this scene is spreading like crazy and will be on the news for a whole entire week and that is free publicity to the max.
Its seems cheap, but the COD gamers do push the envelope in violence, its better than chainsawing random enemy is most gamers.
About adding these scenes for emotion, you are right. After No Russian you as a character really wanted to kill Markharov. Also when General Sheppard killed you and Ghost you wanted to kill him in the end. The story is not great, but I would not call them terribile. Nowhere near the best but its decent.