I think we as viewers can all agree that Gotham has some serious issues. Let's face it, had the show not been greenlit for an early season 2 renewal, I'd say there's only a 50/50 chance it'd still be on the air today. One of the show's major problems lies with the outrageous and unwelcome creative liberties the creators have taken with Barbara Kean.
So Far, So Good
In the beginning, she was presented as the Barbara Kean everyone knew and loved from the Batman comics - always at Jim's side, deeply in love with him, and fully committed to being a model citizen. As the show progressed during season one, things started to shift slightly. It was welcome at first with Barbara getting her own conflicting backstory with past romantic relationships and typical suburban rich family dysfunction.
"This Will Be Taboo, Let's Do It Guys"
Barbara, unable to cope with Jim's career troubles, fled from his side and into the arms of her former lover, Detective Renee Montoya. Despite having incredibly strong feelings for Barbara, Montoya realized that they were no good together, never were. Barbara took this as a rejection and fled from Montoya as well and to the arms of her loving (kind of) parents.
We Get It....
The cliche parents who only care for their money and reputation (boring) was, of course, the most typical way to explain Barbara's inner struggles. I'll hand this one to her, yeah, her parents sucked. They were downright awful people and nobody gave a crap when they died. When I say nobody gave a crap, I meant the audience, not the fictional characters of Gotham.
Heart Broken....Life Ruined
The introduction of Arkham physician and resident Famke Janssen lookalike, Dr. Lee Thompkins, took the direction of the show even further from the lore of the comic books. In the comics, Dr. Thompkins is the female equivalent of Alfred Pennyworth, the maternal figure to Alfred's paternal one. She is a close friend of the Wayne family and often looks after Bruce, giving him advice and making sure he's well taken care of. I guess the creative team didn't really care much for that approach. Instead, they made her an Arkham resident and an obvious flirt/love interest for the recently heartbroken Jim Gordon. And of course, Barbara had to walk in on their epic first public makeout session at GCPD HQ.
And Then This Happened...
Ugh...seriously Gotham? At first, it was an okay storyline to pursue. The audience believed this would be the climactic moment when Jim realized just how much he loved Barbara and he would come valiantly to her rescue. I'm going to take a shot in the dark and say the creators of Gotham have spent too much time watching Game Of Thrones. They said to themselves, "Nah, let's have The Ogre manipulate Barbara into murdering her asshole parents! Yeah, that won't completely backfire when we disregard every little thing about Batman comic lore!"
She's Okay...Wait, No She's Not...
Instead of going the obvious direction with Jason Lennon (AKA The Ogre) taking the fall for murdering Barbara's parents (ugh..god damn it), Barbara confesses to the murder. And because the writers clearly want everyone watching to despise her beyond belief, she attacks Dr. Thompkins with a knife but is subdued before she can actually do any real harm. What's the obvious result of this? Well, everyone hates Barbara now and any real chance of her and Jim getting back together is nowhere near the realm of possibility.
So...Can She Be Redeemed for Her Horrible Acts?
It really depends on how the Gotham team handles it. Can she somehow come to terms with what she's doing and realize it's beyond wrong? Yes. Is there a way to do that without the audience switching their TV's off? Yes. Is there any possible and believable way this can be turned around so that Barbara and Jim end up together after all? Hell no. Should Barbara find her redemption and then vanish from the show's main cast? Yes.
The best thing to do, if the team is to rekindle that remote spark of love the audience once had for Barbara, is to have her face her demons, do the right thing, and then disappear forever. Have her start over in a new town with a new life, let her be happy, have her send a postcard from wherever the hell she ends up. And finally, DO NOT TURN HER INTO THE JOKER. OR HARLEY QUINN. You're not allowed to ruin two characters in one show.
Let her go. It's what's best.