Felix,
Most of what I have learned about Catherine is through this website and other sites discussing the Romanovs, though I do have an outline of the Schneider (or von Schneider) line, taken from which I obtained from a distant cousin of my husband, who lives in St Petersburg. This outline shows Catherine (Ekaterina) as being the daughter of Adolph-Wilhelm born in 1838. However, according to a journal belonging to my husband's grandfather, Edouard-Adolphe (Adolph's younger brother) born 1858, Catherine (nickname Katinka), is referred to as his cousin, daughter of his father's brother, Adolph. Too many Adolphs!
Anyway, Catherine was born in 1866 and was educated in England and Germany, particularly Darmstadt. Edouard 's journal mentions that she also taught the Grand Duchess Elisabeth Feodorovna.
The Schneider family received Russian nobility status in 1868 under Auguste Wilhelm, father of Adolph and Edouard. He was married to Catherine Rachette, grand daughter of Jacques-Dominique Rachette, the French porcleain artist who was "recruited" by Catherine the Great in 1779. JD stayed in Russia until his death so all his children were raised in St Petersburg.
Auguste was a university professor and a state councillor. He was born in Reval Estonia but I don't know why he ended up in Russia.
I hope this hasn't been too confusing.