I think that your selection of Lady Bracknell’s interview and the tea-time with Gwendolen and Cecily’s fighting over a fictional “Earnest” are both great selections!
There are numerous scenes from Oscar Wilde’s play “The Importance of Being Earnest” that continue to resonate with modern audiences. In the performances of this play that I’ve seen, Algernon’s ravenous appetite for cucumber sandwiches and his subsequent cover-up for his guests draws lots of laughter. You could also explore the interaction between Miss Prism and Canon Chasuble, a scene laden with innuendo and made even more humorous by the situational irony of an uptight teacher flirting so boldly with a parish priest. A third scene that seems to garner laughter is when Jack reveals his background: being found in a handbag at the train station.
Although this isn’t exactly a single scene from the play, my students have always found the concept of “Bunburying” to be particularly funny. They claim that it is relatable; most of them have done it, in some form, themselves! In a sense, the advent of technological communication has made “Bunburying” even more prevalent, and you could explore this as an example of how The Importance of Being Earnest” is still enjoyable for modern audiences.
Finally, what makes this play so funny for modern audiences is not the plot, but rather Oscar Wilde’s ironic and witty dialogue. There are so many witticisms peppered through the play that it is difficult to choose a few to recommend, but here are a few that are as funny today as when they were written:
“I never travel without my diary. One should always have something sensational to read in the train.”
“If I am occasionally a little over-dressed, I make up for it by being always immensely over-educated.”
“I hope you have not been leading a double life, pretending to be wicked and being good all the time. That would be hypocrisy.”
I hope this helps gives you a few ideas as you attempt to discuss why “The Importance of Being Earnest” is still a great play to read, view, and perform today!