It was clear from the first time they met that Regina wanted to be rid of Emma as soon as possible. Seeing Ms. Swan as a threat to her relationship with Henry, she made it very clear to Emma that she wasn't needed or wanted, and should be on her way back to Boston. At first, Emma was happy to leave, so long as Henry was well cared-for, but when her lie-detecting "super power" told her that Regina didn't truly love Henry, she decided to stay for a while longer.