Yep get rid of her asap. Sounds like you dont have any power or say in the relationship and this will end up being your fault.
The fact that she has been arranging her next boyfriend right in front of you is shameless. Just dump her and move on, its not worth dwelling on really. Anyone who does that is quite sad and insecure I would have thought.
I never understood people that always had to have a girlfriend or boyfriend. Just went from one to another seamlessly. Sign of an empty life where your self esteem is acquired from feeling power over someones feelings and being wanted by the opposite sex.
My auntie was like this but unfortunately it always catches up with you and one day this girl will end up with no one when she needs them most. So be happy in the knowledge that this next poor chap will just be one of a nice long list of men she has ******.
Oh and ignore the advice to take this up with the new bloke, its not worth it. It wont go well.