Thank you for using JustAnswer.
I'm sorry to hear about your situation. Yes, they have to give you written notice detailing the reasons for denial. This is under county ordinance, not state law: Section 11A-18.1 of the Code of Miami-Dade County, Florida Sec. 11A-18.1. Required notices in connection with application to purchase or rent a dwelling.
(a) Within fifteen (15) days after receipt of any incomplete or incorrectly completed application (or amended application) to purchase or rent a dwelling, the condominium association, homeowners’ association, or cooperative association shall provide the applicant with written notice specifically identifying any and all items in the application that need to be completed or corrected.
(b) Within forty-five (45) days after receipt of a correctly completed application, the condominium association, homeowners’ association, or cooperative association shall either reject or approve the application and shall provide the applicant with written notice of same. If the application is rejected, the written notice must state with specificity each reason for the rejection.
(c) If the condominium association, homeowners' association, or cooperative association fails to comply with the provisions of Sec. 11A-18.1 (a) and (b), of this article, the Director or the Commission may send a demand letter requesting that the condominium association, homeowners' association, or cooperative association, within ten (10) days after the date of the demand letter, provide to the applicant and the Director or the Commission a written acknowledgement of application receipt, notice of approval or rejection of the application, and notice specifying each reason for the rejection (if applicable). The failure of the condominium association, homeowners' association, or cooperative association to timely comply with this provision may be considered in determining whether reasonable cause exists to believe the association's decision or action was discriminatory.
So written notice does need to be given to you, and you can contact the condo specifying this regulation that they have to comply with (otherwise you can file a complaint with the Commission on Human Rights: http://www.miamidade.gov/humanrights/)
As far as suing someone, they do generally speaking have discretion to make these rules, so long as they're not discriminating against you based on race, age, religion, gender, etc... But if your ex told lies about you, you could have a case for defamation. Defamation is a false statement of material fact communicated to a third party that causes quantifiable economic damages to you. So if she lied about you, stating materially false statements of "fact" (not opinion) and that caused you to be denied, AND you could establish the actual economic damages you incurred as a result, then you could sue her successfully.
Hope that clears things up a bit. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable. Please note that I don't get any credit for my answer unless and until you rate it a 3, 4, 5 (good or better). Thank you, ***** ***** luck to you!