i don't think you should tell her parents.. she has confined in you.. i think she has spoken to you about her situation to help her free herself from the mental turmoil that she has been through.. she is probably feeling confused, afraid, angry, trapped and blaming herself for what is happening.
Abuse tends to escalate over time, when someone uses abuse and violence against a partner, it is always part of a larger pattern to try to control her..
Your cousin is probably afraid to leave.. leaving can sometimes be dangerous and there are probably many factors that her abusive partner is using to keep her from leaving the relationship. Tracey understanding these issues can better assist you to help your cousin out of an abusive relationship... try to get all the facts about relationship abuse and the resources available.. make sure your cousin has a personal safety plan for herself if she needs to leave suddenly and where she can go safely for help. here the number for the 24 hour helpline 1800 200 526 to talk with experienced counsellors, she can also call the 24 hour Kids Help Line on 1800 551 800, she doesn't have to give her name and she can request either female or male..