A/N: AU story of how I'd wish the finale to go.
Emily and Hotch got married after 04x06 in Vegas, they decided that they should give it a try and stay married see where it goes, they stayed together till Foyet's attack, when Hotch decided to end it because he didn't want to make her a target.
They got back together after episode "Exit Wounds" and tried again, when Doyle almost killed Emily, Hotch thought that Emily didn't trust him enough, and probably didn't love him as much as he did, since she didn't tell him about it and throws their wedding bands on the floor, JJ gets them and gives them back to Emily when they fly to Paris (6x18).
Although he regrets this and plans on talking to Emily when she comes back, he doesn't when she acts as if nothing happened. In the meantime he meets Beth and decides to give their relationship a try after he hears JJ and Emily talk about a date she had. He still tells Beth that although he is separated he is not divorced and doesn't plan on asking for one, not yet at least.
Emily leaves for London, and although Hotch realizes that his relationship with Beth is just a rebound he doesn't end it because he doesn't want to be alone, and because it takes his mind away from his second failed marriage.
When Strauss dies (season 8 finale) Emily comes back to the states but no one in the team knows, she goes to Rossi's cabin and they talk. She tells him about everything that happened with Aaron in the last four years, from the moment they started dating (after "The Angel Maker" 4x2) since today and gives him an envelope with the divorce papers and a letter for Aaron. She asks him to give them to him because she can't face him and still go through with it but also doesn't want to have the papers served to him at work like Haley did. Dave promises that he will give them to Aaron, but waits will much later to do so.
When Hotch is in the hospital for the internal bleeding (9x5 "Route 66") Penelope calls Emily who is in the next flight over, she goes to the hospital but when she sees Beth there she leaves, on her way out of the hospital Dave spots her leaving and sees that she looks like crying and gets mad. He drives home and gets the envelope with the divorce papers which he still didn't give to Hotch and drives back. He finds Beth there and asks her to give them some time because he has something important to tell to his friend. She leaves them alone and Hotch asks him what happened angrily, Dave (whose been trying to get Hotch to talk to Emily and give their relationship another try because he knows they both love each other to death) throws the envelope on his bed and tells him that he is an idiot and that this time he really screw it up.
Beth comes back in the room as soon as Dave leaves, but Hotch doesn't tell her about the file lying that it's about the case. Later (around episode 9x10) Beth finds the papers on his desk at home and they get into a fight, she asks Hotch why he didn't sign the papers if he loves her and he does it out of anger, she tells him that if he did he wouldn't have needed her to tell him to sign them and she tells him that she had an offer from Hong Kong, and although she didn't plan on taking it she will because apparently she has nothing to keep her in the states.
Hotch doesn't t file the papers and decides to talk to Emily and find out if she really wants this or not, but as many times as he calls her the phone goes on voicemail and his emails go unnoticed, before "200" he finds a letter in the file with the papers, from Emily in which she apologizes for not facing him and tells him that she will always love him because e he is the love of her life although she is not the love of his. He decides to call her again but before he does so, JJ gets abducted.
After they find JJ and Cruz, Hotch tells Emily that they need to talk, so they go to his office and he tells her that he doesn't want to get a divorce from her, because she was wrong, she is the love of his life. He rips the papers in front of her and tells her that he is not going to go through with it, although at first he thought of doing it because that's what she wanted, so if she really wants to get a divorce she should get another batch of the papers but he wasn't going to sign tells him that she isn't coming back and he tells her that he is still willing to give it a try and maybe they can go slow this time, try rebuild a relationship and forget all about their marriage, fix their relationship first.
They keep it secret from the team that they are back together (except Dave, because Dave knows! 10x10) till "Nelson's Sparrow" when Emily comes back for Gideon's funeral and the team has a get together at Rossi's to talk about the memories they had with him. Emily and Hotch manage to work everything out perfectly in the end but Emily still refuses to come back, but tells Hotch to keep asking her because one day she'll say yes. It's like their ongoing thing, every time he sees her he asks her if she's ready to come home yet and every time she says "no".
At Derek and Savannah's wedding she tells him "Maybe" and in "Tribute" she tells him "Yes." After the episode Emily goes back to London to resign and settle her affairs and Hotch works things out with Cruz about her return to the BAU.
That's the back story (if you'd like to see any of it as a story please let me know!), so when Hotch gets arrested Emily comes back to the states earlier than she expected to help the team prove his innocence.