The White Horse / Elizabeth Coatsworth

After one adventurous, but fairly safe voyage, Aunt Nannie reluctantly allows Sally to sail away again, this time into the Mediterranean Sea—and right into the clutches of the Barbary Coast pirates. Taken captive, Sally is exposed to a way of life very different from the protected one she has known. Her resiliency as well as her courage and love are sorely tried; however, both she and those she encounters in the Sultan’s palace will never be quite the same for her stay there.

This is the fourth book in the Sally Series.  The first book in the series is Away Goes Sally (out of print).  The second book in the series is Five Bushel Farm (out of print).  The third book in the series is The Fair American.  The fifth book in the series is The Wonderful Day.