I would agree with your perception of Harriet's character, Reeba. Emma fears that her influence over Harriet's decision will lose effect whenever Harriet is away from her, and actually invites Harriet to stay overnight at Hartfield until she is convinced that Harriet has changed allegiance from Robert Martin to Mr Elton:

"The looking over his letter again, in replying to it, had such a softening tendency, that it was particularly necessary to brace her up with a few decisive expressions; and she was so very much concerned at the idea of making him unhappy, and thought so much of what his mother and sisters would think and say, and was so anxious that they should not fancy her ungrateful, that Emma believed if the young man had come in her way at that moment, he would have been accepted after all." (Ch.7)"

"Harriet slept at Hartfield that night. For some weeks past she had been spending more than half her time there, and gradually getting to have a bed-room appropriated to herself; and Emma judged it best in every respect, safest and kindest, to keep her with them as much as possible just at present." (Ch. 8)