Tatiana was called "The Governess" because she was the most regal and tended to be a bit bossy. Many people said that "You knew you were in the presence of a Grand Duchess when you were with her". She was the one who took her place as Grand Duchess as important, with the usual responsibilities.
And she listened to her Mama most. If she wanted Tatiana to marry Alexander of Serbia, Tatiana would probably have thought something like "If this is for the good of the Empire, and if Mama suggests it, it can't be too bad, can it?" Tatiana just had less of a "fighting" spirit than Olga.