"In 1867 Alabama began granting pensions to Confederate veterans who had lost arms or legs. In 1886 the State began granting pensions to veterans' widows. In 1891 the law was amended to grant pensions to indigent veterans or their widows."

I can see two reasons she was denied pension in husband no. 2s name, first that she didn't qualify as being indigent. I would not think the second marriage would have been the reason. Remarrying would have disqualified her re husband no. 1.

Secondly, the second husband may not have been eligible for a variety or reasons, one could have been taking the oath of allegiance to the United States before the end of the war.