This is a really common problem when you have three people. Two people will make a close connection and leave the other one feeling like the third wheel.
People tend to cut others down to make themselves feel better. That's not news. I had a friend who did something similar, except that if I agreed with her on any point ("Yeah, Renee's shirt wasn't my favorite color") she'd run back and tell Renee I was insulting her. Which is - you said it! - childish.
If you all really want her to move out and it's settled, then your only problem is breaking it to her gently. But I think it may be a good idea to sit down with her and tell her that she is being very negative and that's it's making you uncomfortable.
(There's a cheesy technique that Psychologists call the "I-Message" which is when you tell someone "I feel ____ when you _____.")
Ask her why she feels like she has to be so negative and bash everyone all the time. She may not realize that she's doing it so much - she is probably upset that she is the "third wheel" and wants to "convince" you that Jill is lame so that you spend more time with her.
She may try to make an effort to act more civilly, or she may not. If her behavior doesn't change, and it is still upsetting to the rest of your housemates, then you should tell her you gave her a chance, but you are all still unhappy with her living with you, and tell her you want her to move out.