I haven't heard of Archduchess Elmerice before, but I looked at the photos and she appears to be quite likeable.
How is she related to Archduke Karl?
They are far-away related. Archduke Karl of Austria, the present head of the House of Habsburg and Countess Elmerice both
Emperor Leopold II as an ancestor.
Leopold II von Habsburg-Lothringen, Emperor of Austria, Grand Duke of Tuscany
x María Luisa de Bourbon, Infanta de España
= Franz von Habsburg-Lothringen
Franz I von Habsburg-Lothringen, Emperor of Austria
x Maria Theresia de Bourbon, Princess of the Two Sicilies
= Franz Karl von Habsburg-Lothringen
Franz-Karl von Habsburg-Lothringen, Archduke of Austria
x Sophie Friederike, Princess of Bavaria
= Karl Ludwig von Habsburg-Lothringen
Karl Ludwig von Habsburg-Lothringen, Archduke of Austria
x Maria Annunciata de Bourbon, Princess of the Two Sicilies
= Otto Franz Joseph von Habsburg-Lothringen
Otto Franz Joseph von Habsburg-Lothringen, Archduke of Austria
x Maria Josepha, Princess of Sachsen
= Karl von Habsburg-Lothringen
Karl I von Habsburg-Lothringen, Emperor of Austria
x Zita de Bourbon, Princess of Parma
= Otto von Habsburg-Lothringen
Otto von Habsburg-Lothringen, Archduke of Austria
x Regina, Princess of Sachsen-Meiningen
= Karl von Habsburg-Lothringen
Karl von Habsburg-Lothringen, Archduke of Austria
x Francesca, Baroness Thyssen-Bornemisza de Kászon
= Ferdinand von Habsburg Lothringen
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Leopold II von Habsburg-Lothringen, Emperor of Austria, Grand Duke of Tuscany
x María Luisa de Borbón, Infanta de España
= Ferdinand von Habsburg-Lothringen
Ferdinand III von Habsburg-Lothringen, Archduke of Austria, Grand Duke of Tuscany
x Luisa de Borbón-Dos Sicilias
= Leopold II von Habsburg-Lothringen
Leopold II von Habsburg-Lothringen, Archduke of Austria, Grand Duke of Tuscany
x María Antonia de Borbón-Dos Sicilias
= Heinrich von Habsburg-Lothringen
Heinrich von Habsburg-Lothringen, Archduke of Austria, Prince of Tuscany (1878-1969)
x Karolina Ludescher (1883-1981)
= Heinrich von Habsburg-Lothringen
Heinrich
Graf von Habsburg-Lothringen (1908-1968)
x Helvig Schütte (1910-1990)
= Christoph
Christoph
Graf von Habsburg-Lothringen (1944)
x Ebba von Mohrenschild (1949)
= Elmerice
Elmerice Gräfin von Habsburg-Lothringen (1984)
x Alexander Fairfax