Complex sentence: During his time in Vienna she kept her household in the Palais Kaunitz and it was at this time that Dorothea began to play a major part in Charles-Maurice's life, accompanying him to the Congress of Vienna and probably becoming his mistress sometime after 1815.
Split into simpler sentences: During his time in Vienna she kept her household in the Palais Kaunitz and it was at this time that Dorothea began to play a major part in Charles-Maurice's life. She accompanied him to the Congress of Vienna, and it is even alleged that she became his mistress sometime after 1815.