Please help me get rid of my "friend"?

First you should not hide your feelings about Jade's behavior from Jade. If you are upset about Jade's behavior with your family you should calmly tell Jade exactly what it is that you did not like. If Jade does not apologize or try to make amends to her selfish behavior or at least, explain her attitude,only then should you consider excluding her. After that you should also tell Cathy and Liz that you have put Jade on notice and tell them outright that you do not wish to be in the company of Jade at the amusement park. Then, let them make their own decisions about going with Jade. Best wishes.