You don't say how big the two pieces of luggage are, or if you are only going to be in-country for a week, or what time of year this is going to happen. Answers to all those questions may affect some of our responses.
In general, I agree that managing 2 roller bags from the time you leave home until you get settled in your hotel will be very unwieldy. If there is any way you can reduce that to something you can totally manage on your own, you will benefit from it.
Now, at the risk of also being annoying, I will recommend reconsidering the amount of stuff you take. I am 68. My backpacking days are long over. I now travel with one 22" spinner. Because of the wheels, that's a 20" carry-on in terms of capacity. I also take a cross-body messenger bag which I can easily slip over the handle of the spinner for taking through the airport, train station, or whatever. I am gone for at least 4 weeks per trip with that, and I am a 5'8" XXL person. With good wardrobe coordination, you can pack lighter.
I don't know what the theatre tour people are telling you, or what time of day you will be seeing the shows, but our experience indicated that "dressing up" for the theatre is not very common. Others may have different experience.
Sometimes it's hard to visualize how it would be possible to travel with so little. I think the best source for visual examples, as opposed to a list, is the Vivienne Files (http://theviviennefiles.blogspot.com/?view=classic) Scroll down the right side of the page for the highlighted work, packing. As of now there are 126 posts on the topic which illustrate how you can look great and travel with less. But, in fact, many, including me, take even less than she shows. I hope this direct link to those specific posts will work: http://theviviennefiles.blogspot.com/search/label/packing.
Whatever you decide to do, have a great time and eat some tikka masala for me.