Going back a bit to the dances which were popular in 1911-14, I would be a bit surprised if Nicholas and Alexandra had allowed Olga and Tatiana to dance the more modern dances.
I remember distinctly from reading Virginia Cowles: '1913, the Defiant Swan Song' that there was a craze for the tango in 1913 but it was considered to be bordering on the indecent in polite society. Specifically, Nicholas II forbade Russian officers to dance the tango in uniform (which meant in practice that they couldn't dance the tango in Russia at all, but only when abroad and so in civilian clothes). The Kaiser also put a ban on the tango, and there was a scandal in Berlin when someone held a tango tea in the Reichstag reception rooms.
But there were still the waltz, the polka, the polonaise, the mazurka and variations thereon. From what I have read of Tolstoy, the Russians placed great store on the mazurka - does anyone know why?
Ann