For Ernestine's parents names, I found a Ernestine Lutke (17, b. Mi) in Detroit, Mi. in the 1910 census. She is listed as a "step-daughter". Her mother's name is Matilda.
She has a sister - Millie, 15, b. MI. and a brother William 13, b. Mi. Both parents born in Germany.
ED: 278, page 25A - 1910 Michigan census, Wayne county
Does this match?