It takes two to tango

I don't have a problem with the existence of two islands. At least to my eye, it seems pretty clear that the jet crashed on the big main island, the one where the Others have their Stuckeyville town. But currently Jack, Kate and Sawyer are held captive on the smaller, Alcatraz island, which is where the Others have a workshop of sorts.
As to the whole killing of Sawyer thing, I get the feeling it's not a case of the Others as a whole wanting him dead, but are willing to let Mr. Colleen kill Sawyer out of revenge/grief. I think: the Others need Jack because of Benry's tumor; they also took Kate and Sawyer as leverage to get Jack to do what they want. Then with Colleen dying, the grieving hubby needed to lash out at someone at smirking Sawyer was a perfect target and the Others were not going to stand in the way very much.