My mother has a home in Florida, I am the guardian. Some of the family members have moved into her home against her wishes. How do I get them out?

Chapter 83 Florida Statutes\

You have to give them a written 3 day notice to evict. Then if they do not leave you have to go to court and file another 3 day eviction notice.
I am not sure if the 3 days is for non paying renters only. You may have to check with the court as to how many days notice you have to give for people that moved in on you without a lease.

Florida Evictions (http://www.rentlaw.com/eviction/floridaeviction.htm)

Since they don't have a lease, they aren't really non paying tenants. However, depending on how long they've lived you probably have to evict. Floride a law allows a 15 day vacate notice. So I would have them given a written notice to vacate within 15 days or you will go to court for an eviction order. If they don't vacate, then file for eviction.

First also please watch your wording, there is no such thing as a squatter, and that term gives some people some belief of "rights"

So how did they move in against her wishes, break the door down ? Break a window open to get in.