Hijab

Permissibility presupposes possibility, and it is generally not possible to force someone in their late teens or beyond to do something, except when they are physically in your presence.

Assuming your daughter has her own life outside the home (for instance, attending school or university, a job, socializing, or that sort of thing), it is unlikely that you could successfully force her to wear hijab; often, people of that age in that situation will simply wear hijab when going out the door and then take it off once they get to school, or wherever.

(An exception would be in a place where wearing hijab is the norm, and not wearing hijab outdoors would attract a lot of attention, in which case I would definitely consider it prudent to push a young woman to wear hijab, but I am assuming that this is not your situation.)

As you say, adults react poorly to compulsion, and will usually turn against anything they are forced to do. 

While this may or may not be relevant, it is worth keeping in mind that women sometimes change their hairstyles (or hijab-styles) as a reflection of other life changes - such a change in family status (a broken engagement, a parent's divorce/remarriage, etc), a change in their inner outlook and sense of who they are, or life challenges. So, sometimes, the hijab in and of itself is not really the main thing that is going on, even if it is the most visible one.

It might be worth interrogating why hijab is leading to a dislike of Islam itself. Are there women around who wear hijab who are behaving poorly? Are you living in a place where hijab is stigmatized? Does she just want to express herself more through her clothes or live a different kind of lifestyle? Is it just teenage rebellion? There are all sorts of scenarios, many of which have nothing to do with actual fiqh rulings about hijab.

In any case, discussing the underlying issues - which hijab is often symbolic of - and trying to come to some sort of agreement with her about her clothing might be more fruitful. 

The main underlying purpose behind hijab seems to be discouraging harassment or misconduct from men and encouraging modest interactions. 

When it comes to protecting girls from sexual harassment or indecent conduct from men, I certainly don't think that a girl has to be mature enough to understand things that her parents tell her to do. For instance, parents might tell a child not to wear certain things in public, not to go certain places alone, not to talk to certain people, not to get into a car with a stranger, not to talk to strangers online, etc. 

The parents say these things because the child isn't usually old enough to understand them.

Of course boys should be protected too, but usually there is an extra concern about girls. 

Obviously the hijab does not wholly prevent harassment or misconduct, and it is wrong to say that it does, but since discouraging harassment and encouraging modest interactions seems to be the underlying purpose behind it, this is the angle I am responding from.

There are other things surrounding the hijab such as presenting one's identity as a Muslim. Most children who are nine years old are able to understand that and verbalize it to others (e.g. "I wear hijab because I am Muslim") if they have been raised in a religious family or environment. 

Of course, I understand that hijab can be stressful in a minority situation and there may be things that the child is not yet ready to handle, such as Islamophobia or bullying. This might be a different situation. However, these are more situation-related, not related to the main idea of hijab.