No it's not normal. She does it to get attention and because she is angry and cannot express it any other way.
You can't stop it. She has to do that. But you CAN continue to let her know that it is not acceptable behavior. When she starts it, remain calm, do not raise your voice. Tell her until she can act more maturely, that you will not talk to her. Then tell her to go to her room. If she refuses, then you and the rest of the family (if necessary) leave the room and leave her there to pitch a fit.
When she is done, she needs to apologize and say out loud exactly what she did that was wrong and WHY it was wrong. THEN and only then do you give her any attention.
I suspect that she has anger issues due to the divorce. And she probably pulls this crap with her mother and poor mom just gives in to shut her up.
Don't give in on this! You have to be MORE stubborn than her. And keep enforcing the rules. But it's important that you don't raise your voice or even appear to be upset by it. Act like her fit is no big deal, but it IS against the rules. If you stop paying any attention to her fits, eventually she will realize that it isn't having any effect on her.
I have a girlfriend who was widowed very young and raised her little girl on her own (the girl is now getting her master's degree) Anway she was about 12 or 13 and she tried to pull that same thing. Screaming, slamming doors etc. My friend very calmly waited until she stopped. Then, when everything was calm, she took her by the hand and led her outside to the porch. She explained that this was where she was going to be sleeping from now on. The girl was shocked and want to know why. My friend, very sweetly explaind that since she was acting like an animal, that was where animals slept...outside. She gave her a blanket and pillow and kissed her goodnight and went inside and left her there. After about 10 minutes, a tearful little girl came in with a big apology. She was forgiven and all was well. The lesson was learned.
Of course, there is a time that you need to have a show of force. This same woman I know once responded to the slamming of the door by her daughter (16 at that time) by kicking it in and grabbing her daughter by her long pony tail and reminding her that "she brought her into the world and she was going to take her out!". When her daughter threatened to call the authorities, she said " Fine, then I will make GOOD and SURE they have a reason to take you by the time they get here!.
She got the message. And my friend NEVER fixed the hole in the door....just as a reminder.
*** where is Dad in all this? why isn't he stepping in and laying down the law with her?**** Most likely, it's HIM she's mad at anyway. He should be meeting with his ex and discussing it with her. If they have any kind of decent relationship regarding their daughter, they should sit her down together and let her know that this behavior will not be tolerated at EITHER house. Once she sees a united front, she'll get the message.
If the ex won't work with you, you'll just have to do the best you can. In the long run, she'l respect you more than her own mother for helping her to become someone pleasant instead of an out of control brat!
good luck!