I have cousin in Florida and her daughter and 2 grandchildren live with her. She has had a lot of problems with her daughter and has had the law there many times. She just recently was beaten by her daughter and went to the police station to have her removed from the household. The police told her that nothing could be done because her daughter receives mail there and that makes it just as much her residence as my cousins. What can we do to get her out of this home legally? Please help this case is getting very dangerous.

It is true the police can't make her leave if she gets mail there.
Go to the local magistrate or courthouse and file eviction papers against her
Stating abuse as the reason since it doesn't seem like rent agreement is the issue.

Did the police take a police report on the beating? Get a copy of the report and go to the DA's office and press charges for domestic violence against the daughter. If she is beaten again have the police haul her away and file domestic violence charges. No parent should endure a beating from a child like that.

You file a police report and press changes, if this is life threatening, who gieves a flip on completely legal, you change the locks and set her stuff out, and then let her sue you if she wants to, so you lose a little money if she wins in court, who cares, don't pay and see if she can make you pay.
See the 100's of stories here on people who win in court and still can't get their money.

The number one thing is your safety, so throw them out and the police can't make you let her back in either. Since this is a then a civil issue not criminal.