What is the way to rectify the situation of sending messages to the married female cousin, which caused family problems, along with the desire to restore kinship ties and repent to Allah?

You have committed several sins by corresponding with your cousin's daughter, including violating the sanctity of her husband, putting yourself in doubtful situations, and causing the severing of kinship ties. Your duty is to: hasten to sincere repentance, completely cut off your relationship with her, apologize to your uncle, and involve righteous people if he rejects your apology.