One reason the Lusitania sank so quickly is because she was carrying gun cotton, which explodes upon contact with water. This is the most likely explanation for the second explosion.
The other issue with the Titanic sinking, however, is that, while women and children were certainly the first ones into the lifeboats, they were by and large the first and second class passengers. The steerage passengers were not allowed on the main deck until the last several minutes the ship was afloat. Many of the lifeboats also left the ship half empty, and more lives could have been saved, had the class distinctions been less rigidly enforced.
As GardenTurtle noted, the Lusitania sank in about 18 minutes, which left little time for observing such niceties.
The Lusitania wreck is in fairly shallow waters, rather like the USS Arizona, and can be seen from the surface.