Like I said, you were misremembering or misunderstanding something. The only reason she let Regina take Henry was because she did believe her when she said she loved him. Otherwise there was no way in Hell she was going to let Regina be his guardian. She still recognized that Regina was an evil bitch and wanted to get Henry away from her, but she didn't suspect that Regina would try to harm him in anyway because of that belief.I guess I should add that Henry needed saving only because Regina didn't love him, therefore could not be a good mother to him, despite her keeping to public standards for physical care and comfort.
Emma wasn't letting anyone be a guardian, Henry was legally adopted and she had no legal rights and she knew it. Nor did she want to take Henry at first. The scene showed Emma changing her mind about staying in Storybrook. Being an evil bitch means nothing about being a mother.