First of all, let me start by saying that I really enjoy your writing. Your sentences are fluent, easy to read and it was fun to go through your text. You have a good feeling for words. But what's missing is a plot and/or a conflict. As much as I want to see Alistair and Cullen having a conversation about the Hero of Ferelden, there isn't a real 'hook'.
I like how you describe Alistair. I think this is well done. But he doesn't change. Even if this is just a scene and a brief moment in Alistair's life, your character should change a little, make a decision, come to an understanding, feel differently about something at the end of your scene/chapter. This only happens to Cullen. Obviusly, not knowing how Solana felt and not being able to tell her how sorry he was is something that was haunting him (Cullen). And Alistair freed him of that, so he is in a better place after their conversation. But you tell the story from Alistair's point of view and there is no character development for him. We learn nothing new about him. There is no risk, no real problem for him and I think this might the reason why the spark wouldn't ignite.
Alistair wants to talk with Cullen about Solana because
a) he doesn't want the dinner to be unpleasant and
b ) because it's what she had wanted.
Okay, I'm doing a bit of brainstorming here, so bear with me.
a) Why is the dinner important? Is it actually important? I'm sure king Alistair had many unpleasant dinners, so he could just shrug and see it through. He doesn't have to have the conversation with Cullen. So, you could give the dinner more importance, for whatever reason. Maybe because Alistair needs the Inquisitor to help him with the peace negotiation with Orlais. Alistair wants that everything goes as smoothly as possible because he really needs this and Cullen is the Inquisitor's boyfriend. And that's why he doesn't want an unpleasant dinner. Alistair has something to lose here.
b ) This is the emotional aspect. You could create a greater tension if Alistair were reluctant to talk about Solana. You've mentioned in the story that he tries to avoid talking about her, so why don't you play with this a bit more? Why doesn't he he want to talk about her? Because it still hurts? Then maybe Alistair needs some healing, too, and at the end of the scene he learns that he has to let go.
So, here is what you could do: Alistair doesn't want to talk with Cullen about Solana because thinking of her is still painful for him. But he has to because the dinner is so important and Alistair doesn't want Cullen to feel uncomfortable around him.
You could add even more conflict if Cullen isn't playing along right away. Maybe Cullen is embarrassed that Alistair recognised him from the circle. Maybe Cullen saw the way Alistair had looked at Ingrid and is jealous. Maybe because he didn't want Alistair to find out about the lyrium. So, Alistair really wants to set things right but Cullen isn't at all in the mood to talk. And there you have a conflict.
As I said, I was merely brainstorming. You don't have to do any of this but I believe that your story would be even better with a conflict.
It's late here and I'm not sure how much sense I make, so please ask if something is unclear. (Also, me thinks I use the word "maybe" too much. LOL)