That's why it's so hard for me to stroll in and make these decisions for Dorian. The situation is too complicated and nuanced for anyone to get a good read in the 5 minutes that we know Dorian.
As I said, I tend to see the "Don't leave it like this" as more of a suggestion than anything else, based on the tone. Also, while it's certainly not ideal to bring meta information into perspective, you do have to keep in mind that these types of character quests in games are typically one-offs; you make your choices and it's never addressed again. Most of the time there isn't the likelihood that the person can get away to calm down and think things over and then address the issue at some later date.
In this particular case, I think they did a good job of showing that Dorian is NOT influenced by the Inquisitor. Back at Skyhold, the Inquisitor isn't allowed to offer their opinion on the matter, or tell Dorian that he should feel this or that way. Dorian's decision to even think about forgiveness is based on whether he decided to stay and talk with Halward, and that's all. Even when you do pick that option, Dorian asks Halward a question, gets an answer, and then turns about to leave anyway when he gets even more pissed off with Halward's response. It is only after that line that Dorian decides, on his own, to stay, after which the Inquisitor leaves the tavern to give them privacy.
To the man himself, I do take Halward's apology and request for forgiveness as genuine. Whether that means anything in the end is only up to Dorian to decide and I'll not give my opinion on the matter. However, I will say that for a prideful man, a man who thought he was doing right (however myopic that thought was), to admit his wrong and ask for forgiveness is a big step. That is the reason Dorian is stunned when Halward says this.
To be honest, I'm actually more pissed at Halward likening Dorian to himself with his "pride" remark that Dorian relates once back at Skyhold. I do not, for one single instant, believe that he would do to someone he loves what Halward did to him, and I heartily wish I could tell him this. Personal pride is one thing, and Dorian does have this (to a degree), but blatant disregard of another's feelings and well being is another matter entirely.