If you are going to declare Twelfth Night a reflection of Renaissance ideas, you will also want to include the presence of unrequited love. A common conceit in Renaissance drama, unrequited love served as the central conflict for many of the plays written before, during and after the time of Shakespeare.
Many of Shakespeare's romantic comedies feature love that certainly has a hard time finding resolution. Think about Much Ado About Nothing, for example. There are two couples that end up together in that play: Benedick and Beatrice, and Claudio and Hero. Benedick and Beatrice are self-affirmed single people that have both declared there is no such thing as true love, and they have no interest in finding a lifelong mate. Claudio and Hero are a traditional couple, but the villain Don John makes Claudio believe that Hero has been unfaithful. As one might expect, Benedick's heart softens just in time for Beatrice to be able to urge him to clear Hero's name if he wants Beatrice's hand. Everything works out, just in time for a double marriage at the play's end.
Twelfth Night has an even stickier situation, as is detailed above. And while the formulaic happy ending often plays out, it doesn't work that way for everyone this time. Malvolio is still despised and alone at the play's end. Antonio's feelings for Sebastian never receive satisfaction. Orsino and Viola ("Cesario") end up marrying, and Olivia and Sebastian end up together as well -- but Olivia had only proposed to Sebastian, because she thought he looked like Cesario (she had fallen in love with Viola's disguise).
Here are some questions that you can ask your students regarding these ideas:
1. What is it about us as people that makes us treasure happy endings? Why do so many romantic stories end this way?
2. Why do so many romantic stories end at the wedding?
3. What is a movie you have seen that is similar to Twelfth Night in terms of plot and theme? Compare and contrast the two.