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.
