It really shouldn t be all that bad until maybe when you get past Kennedy Airport. The Van Wyck has a tendency of getting jammed up at that spot. Assuming that you are going to take the Outerbridge into Staten Island, over the Verrazano and then the Belt to the Southern State. It takes a good three hours from DC to Staten Island then figure one more hour to Islip.
it s not possible to get to Long Island without going through NYC (not counting taking a ferry from bridgeport CT but that s way out of the way). However, the Goethals bridge, the SI expressway, the Verrizano bridge, the Belt parkway and the southern state are the mots direct.