You are renting the property now correct? That makes you a renter. A renter has certain legal rights. Having a safe back yard may or may not be one of them.
If this is a real rental question why not talk to your local code enforcement office? Ask them about what the rights of a renter are on this issue. Take some pictures with you on a digital camera if possible. That way they see the problem.
Maybe they will send you to another dept. but this is the procedure to use to find out your rights here. You may find out you can legally make them take the tree down, maybe not. If you get a reply saying the tree has to go get it in writing. Then the landlord and realtor can not argue with you.
A landlord refusing to do what is legally required is not good for the landlord.... more