I have no experience working in a hospital, but I have worked in toxic work environments. It's not easy to leave, especially when you hope to turn the experience into something better with the same employer. Here are a few random thoughts.
1. Don't worry about your family member. If the unit has the reputation you say it does, I don't think anyone will form a negative opinion of you or your relative if you decide to leave.
2. In case you haven't seen The Devil Wears Prada, here's the 10-second recap. Young optimistic woman goes to work for a horrible editor who treats her staff terribly. Woman considers leaving but reminds herself that assistants who can stomach working for this woman for just one year "prove" themselves, and editors around the city fall over themselves to hire these assistants. Imagine yourself in the same position. If you can prove to administration that you can handle working in this environment for a year, they will see you as an employee who can handle ANYTHING.
------This is also good advice for new nurses who find themselves in less-than-desirable jobs after graduation, or for those new nurses who are complaining that they can't find a job, but they're only looking for $22 per hour with full medical and dental at facilities within 10 miles. Just get your 1 year in. Take whatever you can get and make the most of it.
------Other valuable lessons from Hollywood movies: don't talk about Fight Club, never say "whew, that was a close one!", and don't kiss on the mouth until you're ready to give up your life of prostitution.
3. Just go in, do your work, and leave. Don't get caught up in the grapevine, and don't take it personally. If you focus on work and don't respond to the gossip (whether it's about you or not) then it's harder for them to make you a target. Maybe they'll say you don't belong there, you don't fit in, you're not a team player, whatever. It's probably true - you DON'T fit in there. But someone has to be there for the patients - they need someone like you looking out for them, and your coworkers are dropping the ball.
4. Focus on finding constructive ways to fix the problems. Is there something the unit manager can try? What policies might help? What training is needed? Even if you don't feel comfortable bringing up your suggestions or if they're never implemented, this type of thinking can help hone your problem-solving and leadership skills, which will be helpful later in your career.
5. Not everyone on the unit can be as poisonous as you think. Some of them may just go along with it because they want to fit in. If you model a different type of behavior, you may find someone else who thinks the atmosphere is appalling and admires your courage in refusing to give in.
6. If they pressure you to conform, try some evasive maneuvers. School works to your advantage. "I can't talk, I need to go practice palpable systolics." "Sorry, I can't eat lunch with you, I have to review my physiology notes for a test." "No, I didn't hear those awful things you were saying about our patient, I've been reciting the cranial nerves in my head."