Yes, your uncle can get divorced. Tell him to get to an attorney, it is so much easier to have someone who does divorces for a living represent him.
R. Jason de Groot, Esq. We do not have an attorney-client relationship. I am not your lawyer. The statements I make do not constitute legal advice. Any statements made by me are based upon the limited facts you have presented, and under the premise that you will consult with a local attorney. This is not an attempt to solicit business. This disclaimer is in addition to any disclaimers that this website has made. I am only licensed in Florida.
Florida is a no-fault state. Your uncle must simply file for divorce stating that the marriage is irretrievably broken and he does not need his wife's consent. He should just file a petition for dissolution of marriage with other requisite documents and serve the same on his wife. It would be prudent for your uncle to consult with an attorney to ensure that his interests are protected.
This communication is for informational purposes only and does not constitute legal advice and does not establish an attorney-client relationship.
He would only need her to sign something if he was trying to do an uncontested dissolution of marriage. Since she has clearly stated that she has no intention of cooperating with his efforts, he needs to file a regular divorce action and have her served with the papers. She will then have 20 days to file a written Answer with the court. if she fails to do so, the Clerk can issue a default and your uncle can schedule a final hearing.
Please note that without more specific information, I am unable to provide a definitive answer to your question. Please accept my answer for informational purposes only and I hope it will give you a starting point in seeking legal representation.