So let me understand you. You want to go kill more of them ( and in the process endanger our military and pi$$ away more more money we’ve had to borrow from China) because they are killing each other. You have some seriously screwed up moral values! Also, in so doing, you are going to help out Al Quaida (sp?)
There is no wrong spelling of Al Qaeda in English. Any spelling with Roman characters(our alphabet) is a transliteration of sounds that aren't even close to English or other European sounds. There is no official spelling for it or any other Arabic word. El Kaida is just as good. The vowel sounds change with regional variations and are not even represented in the Arabic script. The "K" or "q" represents any of several sounds in Arabic that would be recognized as "k" in English. Even the "d" is not so straightforward and depends somewhat on regional variations.
Hussein, Hassan, Hosni, Hosseini et al are all the same name.
A rational case could be made for mounting a rescue operation to take out all the Christians and Jews and maybe even the Alawites and Druzes and Dervishes and the dozen or so Fire Worshipers and then nuking the whole place.