What rights do Ex Husband's Girlfriend have?

My ex and i share 50/50 with my 6 year old son. He just moved in with his girlfriend and they just had a baby. She is now asking to be cc on all emails that i communicate with my ex in regards to my sons medical or school stuff. She also called me (first time ever) 2 days ago and demanded i drop off my son at a set time, and if did not call her back she would take to me court. In addition, my ex had her take my son to a doctors appt that i asked me ex to take him. he did not tell me, and also in advance and signed the paper work at the doctors office to allow her to bring him in, and all of this was done with out my knowledge or consent. She does not know my sons medical history and she should not be there and answering any medical questions.. Im the mother and i should communicate all medical and school questions/concerns, etc to my ex. and only my ex. What right does his new girlfriend have?? And to also threaten me with court?? Did my ex have the right to change med?