Some of the information my grandmother (Edith Eileen Ainslie - Andrews) collected: William Garret Ainslie was born 04/01/1782 in Amsterdam, Holland. He ran away from home at 16 when his father remarried and went to live with his aunt Wilhennia. His family disowned him when he deserted the Dutch Navy. He was in the British Navy during the War of 1812.
By the way Jill. I assume the picture I have of my grandmother's cousin (Eileen Frances Ainslie Pike) would be your mother.