Here is what I know about Mathilde:
She was picked by Alexander III for his son Nicholas because she was beautiful, outgoing, compassionate, and she was a prima ballerina (imperials picked ballerinas for mistresses a lot).
Nicholas was in love with her, but still always in love with Alix. He gave Mathilde jewels and a mansion in which they lived together in for a time.
Nicholas did confess to Alix that he had had an affair with her so that they could have an honest relationship with no skeletons in the closet : ) Alix said it was in the past and that she forgave him.
Mathilde ended up being linked to two more of Nicholas's cousins and since she had a son (born in 1902), the one she assumed was the father, Andrei, married her in 1921, although it is still disputed as to who was his real father. The family moved to Paris where she opened a ballet school. Since Andrei and Sergei were cousins it makes DNA testing even harder.