We come into her story to discover that somehow she's been transformed into a rat, but somehow is able to speak and retain her human intellect. She meets an ambassador from what we'll call the Babylon 5 universe, and through him she gets in contact with some powerful aliens who are able to return her to her human form. The problem here, however, is rather that. Problematic.
Note: Babylon 5, Londo Mollari, Centauri, and anything else from that entire universe is a copyright of J. Michael Straczinsky, Babylonian Productions, Warner Bros Inc.
Now, the ambassador in question is Londo Mollari and his "friends" (note the quotation marks) are called the Shadow (ancient aliens who seem to be able to grant almost any wish....but in return ask for sometimes truly horrific repayments in return). She gets caught up in a situation very much like what is seen in the TV show . The ambassador is involved in a intricate (delicate) plot to assassinate the current (quiet barmy) Emperor of Centauri in order to save the planet from the backlash the Emperor has forged between that planet and the Shadow. If left alone, this alliance will result in the destruction from either their "allies" or the Shadow's enemy (another ancient alien race called the Vorlons).
Well, as per what happened in the TV show, the Emperor is killed, but in the chaos Stacy decides that things have gotten too out of hand (and too dirty for her likings...and a little sore still at Mollari for telling the Emperor that she was his slave, even though it was to save their lives), so she makes a break for it into the hills of Narn (see the suggested website for more info below for that and other topics related to Babylon 5. However, before making good her escape she runs into the representative of the Shadow (a Mr. Morden), who has come to collect on that debt that Stacy owes.
He wants the secrets of time travel and believes that Stacy (who hales from 20th century Earth), can provide that information. so the Shadow could invade Earth in it's past. It is either that information that Stacy must provide, or else she's faced with some kind of other unnamed payment. Not wanting to face that unnamed (obviously creepy and dangerous) task, Stacy decides on the first one. However, not knowing just how she got there (and not really wanting to tell even if she did) she makes up a totally fabrication that....isn't actually very believable (but the best she could do under the pressure of the moment). She basically tells Morden that she came back in the USS Enterprise (NCC-1701), and had a bit of....trouble with the transporters (and got turned into a rat).
At first Morden doesn't believe any of it, but then his masters (the Shadow) interrupt nervously, saying to him that such.....vehicles and technology is possible, but is currently beyond their reach. Shortly after that, all Hell breaks loose!
See, the thing here with Stacy is that she shares something in common with another odd fellow called Scott Chen (the main character from Addventure 3). In this story thread, she has been "infected" with something called "choas energy". It means that odd things happen around her, to her, and to others around her. See, that explains in large part just why a landing party, lead by Spock, had shown up and rescues her from her plight.
It appears that this Enterprise had gotten, while getting slingshot around a black dwarf, gotten dragged through a rift in space and ended up here. They'd gone to this world on Spock's suggestion in search for a way back. Not finding it (and Spock now at a loss as to just why he'd believed that an answer was here), they soon found out from Stacy the situation that this planet faced.
The exact details of how it comes about are a bit involved, but here's the bottom line.
Kirk being the person he is, using a dubious justification at best, decided to interfere with an upcoming battle between the forces of Babylon 5 and the Shadow, and basically cleaned the Shadow's clock! See, the Enterprise is a faster than light vessel with faster than light weaponry in a universe that has, at least in this area of space, no FTL weapons or ships!
Rigthly not trusting the Earth of this reality, Kirk instead soon forged an alliance with those on Centauri, setting up relations between the Federation (i.e. the Enterprise in this case) and the rest of the Babylon 5 reality. Stacy became something of a diplomat between the Federation and Centauri Prime (i.e. the cover story is that she was in the employment of that planet and asked for aid on it's behalf). Some odd synergy happened as well when Lt. Uhura, having looked at some schematics of the jumpgate technology of this reality (they used artificial wormholes of sorts to travel the galaxy) and discovered it looked rather like the communications array she always used in her course of duty. Short of it is that she was able to combine that technology and the use of the Enterprise's FTL drive and something of a Transwarp system was developed. It's the fastest means of interstellar travel (short of LONG wormhole travel) around now! There was reparations and even reconciliation between Narn and Centauri Prime (who'd invaded her and conquered).....Kirk was even able to work a hat trick or three and now something of a grudging friendship between Narn's leader (G'kar) and Mollari (Cenauri's leader) exists. It was considered something of a miracle by some, considering that the two were destined in the TV show to strangle each other to death sooner or later...
Oh, and let us not mention that the Enterprise scared both the Shadow and the Vorlon's so much that they soon decided that it was now a good time to actually leave this galaxy. They'd had plans on doing it anyway after seeing that their duties of "guiding" the younger races was done, but this kind of hastened their plans......
Now, I wish I could say that all lived happily ever after, but I can't.
The Enterprise, after ten years in the Babylon 5 universe, soon attempted a miracle of sorts and tried to get back to it's universe, but instead ended up over Logopolis in Dr. Who's universe. It should have destroyed itself, but Stacy is somehow able to sacrifice herself and saves it.
What happens after that is told somewhat in another story, but that is another story (of course).