I think you're exaggerating. Not all the rebels fighting Gaddafi's forces are Al Quada but it wouldn't surprise me if some were, Al Quada and their sympathizers are in almost every country and political movement in the Middle East. Besides, NATO knows how to deal with Al Quada insurgents, I don't think they'll be playing a major role in rebuilding the gov't when Gaddafi's forces are defeated.
As for the media, they are spineless lackeys to political correctness and leftist bias. They wouldn't be caught dead reporting that certain freedom fighters rebelling against Gaddafi's army may have ties to Al Quada, it would ruin a great story.
On the other hand, if Israel feels that all of these uprisings and coups in the Middle East are going to produce secular governments that operate under Sharia law, I don't blame them for wanting to protect their own interests, not that I believe Israel has the kind of influence over Muslim nations that you're claiming.
Don't underestimate the strength of America's alliance with Israel, I feel comfortable saying that in meetings even your irrefutable sources don't know about, the US and Israel are working on avoiding a conflict of interest.