that Emma planned the call - silly little Harriet probably asked her advice. After all, she still thinks Emma knows everything and is always right. You are right in thinking she would have done better just to go without telling Emma, but once she does she is sunk. We learn [Emma] "meant to take her in the carriage, leave her at the Abbey Mill, while she drove a little farther, and call for her again so soon, as to allow no time for insidious applications or dangerous recurrences to the past, and give the most decided proof of what degree of intimacy was chosen for the future". It is not at all clear whether she told Harriet all that. I would not put it past her just to offer the carriage and say she would return after a short time.

Emma herself, to her credit, does not feel quite right about this plan in her heart, she sees the ingratitude but "it must be done, or what would become of Harriet?" Yes, Heaven forbid that Harriet should fall into the clutches of a decent and honourable family who, thus far, have shown themselves to be rather better people than Emma is.

So where we are in Chapter 23 is - Harriet is just starting to relax with the Martin ladies when Emma arrives after an exact 15 minutes and summons her - I presume she sends her coachman. Harriet comes to heel at once. I don't see that she has much choice - Emma is sitting out there in the carriage. Should Harriet:

Refuse to leave the house and send a message that she wanted to stay longer and could Emma come back in an hour or so? That would be terribly rude,or.

Send a message saying she wanted to stay longer and would make her own way home. That would be marginally better, but still rude.

Either of these two options would probably end Emma's patronage of Harriet, which the deluded girl values.

Or should Harriet go out to the carriage and argue with Emma for some considerable time (because Emma would not just agree to it) about staying longer. How would she explain that to the Martins? "I'm just going out to ask Miss Woodhouse to let me stay a little longer and may be some time". The only civil response to that would be for the Martins to ask if Miss Woodhouse would condescend to come in, and just think how that would go down with Emma.

Harriet could of couse obey Emma but return the next day and apologise. For not doing that she is culpable - but I am not going to completely absolve Emma for something which she herself, in her heart, knows was wrong.