Here is a link to the page on the National Archives website that contains links to all the Confederate state bureaus, libraries, etc. where the pension application files are located:

http://www.archives.gov/genealogy/military/civil-war/confederate/pension.html

As Alabama issued pensions only to veterans who had lost arms or legs during the war, perhaps that is why the 2d husband wasn't eligible for a pension.

You may want to query the Alabama archives to determine what other criteria were used to determine whether a veteran or his widow received a pension.