I do agree that it was harsh of Emma to do what she did–Regina is also Henry’s son. But Henry himself sought out Regina because he was unhappy and because he wanted to break the curse and save everyone. Regina herself admitted that she wasn’t capable of love for a very long time. I think Emma was still afraid for Henry–Regina has unintentionally poisoned him once due to her rage. She feared his life would be endangered again.
Regina did sort of let Henry go in We Are Both. She realized that the way she was raising Henry was not right and she wanted to show him that she could change.
I think that–if Cora had not showed up–Regina and Emma would have reached the point of both of them being in Henry’s life. He loves both of them and cannot be without the other. And Emma was certainly making the effort before Cora showed up, and so did Regina. Both of them were trying to be civil and polite, even getting close to friendly with each other.