I've been reading a lot about the fascinating last months of the Romanov dynasty, specifically the "forgotten period" between the family's abdication and their execution. I understand that the Empress was not of Russian descent, but would the family not have spoken Russian on a daily basis, being the language of their father, their peers, and their empire?
Nicholas and Alexandra usually spoke English to each other. Their letters to each other were in English. The children spoke Russian to their father and English to their mother, with the common language being English. Alexandra (born Princess Alix of Hesse and by Rhine) was a favorite of her grandmother, Queen Victoria. She spent a lot of time in Britain, especially after her mother died, and spoke fluent English as well as her native German. She seems to have struggled with Russian, which did not endear her with the Russian people.
Nicholas spoke perfect English, with an Oxford accent. He also, like most educated men of the time, spoke French. He also knew German, but apparently not well enough or they just settled on English. The children were also educated in French and some German.
Robert K. Massie, Nicholas and Alexandra