This is a brainvomit of a story. I excel at the rambly bits when I'm tired, and while I don't believe Hatter thinks quite this incoherently, it got a warm reception the first time around, so I figured I might as well keep the incoherent mess and see if a good edit did it any good.
Your patience is much adored.
It takes Hatter two months to build up the nerve to go.
He spends that time very pointedly not thinking of Alice. With the destruction of the Red Queen's tyranny, Jack, in an unprecedented act of either stupidity or generosity, appoints Hatter to the formal role of Advisor. This means that Hatter spends a ton of useless time running around and offering his opinion on things that he rarely actually cares about, but he does get to oversee the renovation of the Library, which turns out alright. He also spends a lot of time visiting Charlie, who eventually opted to stay in his forest and resume his pursuit of Jabberwocks and Bandersnatches. The small remainder of Hatter's spare time goes to picking up the pieces of his ransacked Tea House and figuring out what to do with it, because despite his current, not-insignificant source of income, Hatter really does like tea—rather a lot, actually—and he would like to keep running a Tea House.
Despite all this, though, Hatter still finds himself with time that he can't seem to fill, and he spends that empty time sitting in his chair, often with a cup of tea cooling in his hands, staring at the purple velvet coat draped over his couch. He can't bring himself to hang it up. It's a nuisance, that reminder of what's missing, what he doesn't have, what he let go, but he won't touch it.
At least, not for a week or two. One day, coming home, his fingers brush across the velvet as he passes the couch, and like that, it's routine. It's routine to linger for the barest second, routine to rub his fingertips together to hold the feel of her, something like her, close as he will get to her on his skin and pretend he's not doing it, because Hatter is many things, but he is not a man to long for things he cannot have.
Or so he tells himself. When Hatter thinks—not-thinks—of Alice, he inevitably ends up thinking of her and Jack, of her hugging him and him hugging her and leading her on, which Hatter never did—well maybe a little, but not a lot, and certainly not as much as Jack did—and he is reminded of how she didn't stay, how she didn't linger. He doesn't remember how she more or less told him to come over, how she trusted him in the end and smiled at him and hugged him and god how good that felt because she's through the mirror, now, she's happy, that's not his to intrude on.
And Hatter does a very good job of fooling himself for a very long time. Such a good job, in fact, that when the purple velvet coat ends up draped over the back of his chair, where he can just tilt his head and catch the lovely spicy scent that means Alice, it never even occurs to him that that weight in the back of his throat and quiet roaring in his ears is anything more than absolutely nothing.
He is a master fooler. It takes Charlie to get Hatter to come to his senses, in the form of a quiet muttering over a campfire and Bandersnatch ribs. "When I was a squire," Charlie begins, and Hatter sighs. "When I was a squire, there was this girl. She was a pretty girl. She lived in a village we stayed in for a night. She had long brown hair and a big smile and would look at me in this way when she saw me. I spent all night trying to get up the courage to talk to her, and I'd decided to bring her a pastry in the morning and say something nice when in the middle of the night one of the men got the runs and I had to spend all night and all of the next day taking care of him."
Hatter just looks at Charlie, who stares at the fire, humming quietly. "What?" Hatter asks eventually, and Charlie doesn't seem to hear him. Charlie just sighs, "I miss Alice," and it isn't until after the 'Me, too' gets lost somewhere between his brain and his mouth for the second time that Hatter says "Oh, sod it," stands up, and leaves.
He forgets his uneaten rib, which he regrets.
Hatter has to end up asking the king for help, which he hates, but in all reality despite making an awful first impression Jack is a good guy and a good king. He is also willing to help Hatter go from Wonderland mode to Oysterland mode, though the Duchess—whom he married in the end—doesn't help by making fun of Hatter's hair.
And then he's through the looking glass, and it's dark and damp and cold, and Alice is laying on the ground and not moving, she's not moving and Hatter is terrified. He moves, moves for Alice, stumbles towards light, and noise, and finds a man—in really hideous orange—and gasps, "Come with me."
There was never such a beautiful sound as that man's voice: "She's over here!"
There is a flurry of lights and action and people talking, and it's all Hatter can do to keep tabs on Alice, follow her with his eyes as people in white uniforms check her over and lift her into a great shrieking monster of a vehicle. Someone asks him what happens, asks him his name. It's his natural suavity and charm that keeps him together: His name is David (David? Who's David? Was he a David once? He's a David now, but he's also a Hatter now), he saw her run into (through) the building (Looking Glass), and got worried (was terrified, distraught, stark raving mad, it was the worst two months of his life, and that's not strictly true but at the same time it is so shove it). She was taken to a hospital, to check up on her, they tell him, and he barely catches the name of the place before he's racing off after the ambulance.
He worries the brim of his bowler hat between his hands for hours in the hospital lobby. He doesn't like hospitals, never did—they smell of sterility and dead things—and the fact that Alice is here somewhere and he can't see her is enough to send him off the deep end again.
But he holds on, because he has to, because that's what you do. Some sweet woman—older woman, but not old woman, honey-blonde and smiling—recognizes him, greets him, thanks him, and Hatter (DavidHatterDavid) manages to sound not completely barkers when he talks to her.
And then the woman is gone, and Alice is with her, and HatterDavidHatter follows the taxi.
Not that it's hard. The cab stops a handful of blocks and a half away (slow walk in this traffic) and lets them out, and Hatter hovers at the door, trying very hard not to be suspicious as he sees what mailbox the mom gets the mail from, muttering the number over and over so many times he thinks he might have it burnt onto his tongue. He waits, and hovers at the reflective window, patting down his hair again and again—which is stupid, because he's never really cared about his hair, just about his hat, but Jack made him brush his hair and his bowler looks stupid with brushed hair but he doesn't want to muss it up because what if having brushed hair is incredibly important and they slam the door in his face for having messy hair—and then he gets sick of himself and just goes.
The door bell makes him jump.
The door opening makes him jump, and then wilt a little, because it's the mother, but he barely has to say a word before the old-not-old blue-eyed woman recognizes him.
"Of course," and the mother beams, then ushers him in and calls for Alice. And Alice comes down the hallway, and Hatter turns and sees her, and he thinks he might cry, or scream, or both. Her entire face brightens with recognition, and she gasps his name—Hatter—and then she's hugging him and he's hugging her and this is infinitely infinitely better than the last time, and she's softer than velvet and smells better than he ever dreamed, and all he can say is finally.
She tells him he has no idea how happy she is to see him, but he does, he really does—he knows, because his heart is pounding and exploding and stopping all at once; and then they kiss, and it's perfect, it's perfect.
And he says he missed her. And he did. He really missed her, despite all the busy and the not-thinking and the denial. He didn't realize it for far too long, but he did—every night with the shadow of Alice in that purple velvet coat was torture, and he missed her, but she's here now—and then they kiss again and Hatter knows, knows, that this is right.