Anna sounds like a very interesting person, and I'd love to know more about her. There is an old German book that focuses on her conversion to the Catholic church, but I have yet to obtain a copy. According to Hesse: A Princely German Collection (pg 136), "Hers was to be a lonely life. As the second wife of Friedrich Wilhelm of Hesse-Kassel (after the death of Alexandra Nicolaievna in 1844), Anna was never close to her husband. In 1866 her Prussian family turned against her when Friedrich Wilhelm chose the Austrian side in the Austro-Prussian war. After her husband's death in 1884, she lived out her lonesome years at the summer castle of Fasanerie (one of the few Hessian castles the victorious Prussians allowed the family to keep), retreating in winters to Frankfurt. She was an accomplished pianist who looked to artists for friendship, including Brahms, who dedicated a piano quintet to her, and Hans Christian Anderson, who dedicated an edition of his fairy tales to the lonesome landgrafin."
The same book also states on page 268 that "Brahms said of her that if she weren't born a princess, she could have earned her living as a concert pianist."