No, of course not! Cheating is never justifiable. I understand that you're hurting and she's a complete jerk, so... break up with her! That's the solution! It will make you happier and you should never tolerate someone abusing you like that. I know you want to retaliate for what's she's done to you emotionally and physically, but all you've done is stooped down to a low level, maybe not her level but a pretty low one. Plus, you're thinking lacks maturity. If you're having problems either try to communicate with one another and talk through it and attempt at improving the relationship. However, if the relationship is too toxic and harmful, break up with her and move on. I know you intend to hurt the girlfriend, but in actuality if you are really fond of the girl you're seeing to despite your girlfriend, you actually are hurting her and if she finds out... I'm afraid you will have blown a great chance at a relationship with a girl you do like without cheating on her. You basically are also cheating on the girl who isn't your girlfriend too. This is not ok. You need to fix this.
If she's abusive toward you why are you with her in the first place. Way before cheating I would have broken up with her and given my time to the nicer girl. Why is the nicer girl getting the ugly end of the deal in the first place. Is it justifiable to use her to get revenge? I think not. Move on from your abusuve Girlfriend and make Ms. Nice Girl a better place... Or if you don't like her like that, move and be single and free!
No because you could have broken up with her to pursue the nice girl. Cheating is still immoral and dishonesty as well as unnecessary. So you are definitely wrong for doing it and a bad person in this situation.
No, no! Don't cheat on anyone! Yeah, I agree, this girl sounds awful, but still don't cheat! Break up with her, and openly be with someone who truly likes you for who you are, not constantly jealous over nothing. Nobody deserves to be cheated on, but you should break up with her if you think she does. There's obviously no love in that relationship. Break it off! Good luck!