Butch betrayed the Penguin so there's nothing stopping Osvald from killing Tabitha. Butch is her best chance of survival.
Bambi + Lewis Skolnick = Disney's Peter Parker

Putting the feelings part aside, I am sure that Barbara and Tabitha are going to need some muscle soon, the two can't do it all on their own forever, sure Tabitha has skills but not Barbara so much.

Butch was going to kill Penguin, in part because they were going to kill her if he didn't. So, she see's his loyalty and he's an asset to them for protection. Barbara and Tabitha at some point are going to make a move to try and takeover Gotham.

isn't butch the only one keeping Tabitha alive from Penguin? I forget, they mentioned something about that before >_> XD
I used to be indecisive. Now, I'm not so sure.

Because she likes him! so wish we got to see her actually hijack the ambulance, thought.
Tabby and Butch are honestly one of my favorite pairings on not this show, but any show. So unconventional, with a creepy, kinky backstory and a vibe of true love mixed with "but maybe I might just have to kill you, nah sorry sweetie".
Plus, I really like Butch as a character who was literally "Goon #1" in the first episode and has worked his way up as a character and actor to stand as an equal to The Riddler and The Penguin. Great actor, and a really well developed character who - unlike so many shows' "original characters" doesn't at all feel like a creator's pet or Mary Sue.

Also, since Barbara isn't actually in love with Tabitha, she's not going to be the jealous type and expects that Tabitha has a life outside her.

Tabitha is Barbara's business partner/FWB so she wants to keep her happy and I think she feels Butch can be an asset. Butch does have intimate knowledge of the underground in Gotham especially Peguin's operation. All of that benefit's Barbara as she tries to rise in power herself

But why is Barbara going along with it? What does she can by helping Tabitha rescue Butch and double crossing mayor cobblepot?

She does like him.

Because Tabitha clearly likes Butch.
Really wasn't that hard to figure out was it?

I think she feels possessive towards Butch. She basically made him her creature when she tortured and broke him, and no one is allowed to mess with him except her. She has feelings for him, but they are more like the feelings one has towards a beloved pet than feelings for him as a human being. Likewise, Butch's feelings for her are like those of an extremely loyal puppy towards it's master.

Well it's called feelings gents. Tabitha and Butch have them for each other and they keep looking out for each other.

Your guess is as good as mine, I'm having more and more trouble trying to follow the logic of how these characters behave.

She's clearly got feelings for him.

Literally no idea. I was so confused.