Have you recorded the quit claim deed? A quit claim deed is not actually a deed. It is a "release" of any claims to the property. If your mother intended to make a gift to you, and you record the deed, you become the record owner and you can tell the brother in law to mind his own business.
The response given is not intended to create, nor does it create an ongoing duty to respond to questions. The response does not form an attorney-client relationship, nor is it intended to be anything other than the educated opinion of the author. It should not be relied upon as legal advice. The response given is based upon the limited facts provided by the person asking the question. To the extent additional or different facts exist, the response might possibly change. Attorney is licensed to practice law only in the Commonwealth of Pennsylvania. Responses are based solely on Pennsylvania law unless stated otherwise.
If the property is in Florida, Florida law controls. You need advice from a Florida attorney to make sure the deed was executed properly, that it describes the property correctly, and that other Florida requirements have been satisfied. There are also many, many unintended consequences when real estate ownership is transferred. I hope your mother used a Florida attorney to prepare the deed.
Under Florida, a Quitclaim Deed is a deed and can convey title. It lacks a warranty of title that would be found in a warranty deed, but otherwise can convey title.
One of the many problems with a parent giving property away during their lifetime is that someone call challenge the transfer based upon claims of undue influence or incapacity. If your mother used an attorney, the chances of these arguments should be reduced.
There are so many factual and legal issues involved that no one can give you proper advice without meeting with you and reviewing the facts.
My comments are not intended to establish an attorney-client relationship, are not confidential, and are not intended to constitute legal advice. Proper legal advice can only be given by an attorney who agrees to represent you, who reviews the facts of your specific case, who does not have a conflict of interest preventing the representation, and who is licensed as an attorney in the state where the law applies.