Who is related to both Lady Capulet and the Prince?
Mercutio, Romeo's best friend, is related, by blood, to Prince Escalus. We learn of their connection after the fight in which Tybalt challenges Romeo. Romeo refuses to fight (because he's literally just married Tybalt's cousin, Juliet), so Mercutio fights Tybalt because he believes Romeo dishonors himself by refusing the challenge. Tybalt then kills Mercutio when Romeo comes between them during the fight, and then, finally, Romeo kills Tybalt. After Romeo has fled the scene, the Prince arrives and Benvolio explains what happened. Upon hearing the story, the Prince says,
I have an interest in your hearts' proceeding.
My blood for your rude brawls doth lie a-bleeding. (3.1.150-151)
In so saying, the Prince acknowledges that Mercutio was his relative. Further, Mercutio's family had received an invitation to the party at the Capulets' house, and so this indicates, perhaps, some kind of relationship, even if not familial. Otherwise, I'm not sure who might be related to both the Prince and Lady Capulet. The Count Paris is also related to the Prince, but there is not evidence to suggest a relationship to Lady Capulet.