Because of Quinn's pregnancy, Sarah wanted her to stay with Adrian through this time. Given that he was the father of the child conceived by her. Actually Adrian didn't want to live with the woman who had broken his marriage. But he was forced to accept it, not because of his mother's orders. But rather a greater purpose.
He intends to conduct a DNA test on the child Quinn is carrying when she reaches 8 weeks of pregnancy. So she deliberately accepted Quinn and was nice to her so that when she was taken to the hospital, she wouldn't fight back and make too much noise.
Although Adrian could have forcibly taken her to the hospital, it was a risk to the child Quinn was carrying and he didn't want to take that risk even though the child was not his. His name would be on the line if anything happened to the baby.
"Welcome, Miss Quinn," greeted the servants working in Adrian's home.