Leah,
Your trip sounds amazing and your kids are going to enjoy London. Overall the plan looks doable, however, there are areas that I think you might want to take another look at:
Friday:
- V&A: I love the V&A museum, however, it is huge. Before going, I would recommend looking at the areas of interest for your family to narrow down the galleries you would like to visit. The theatre gallery is fun and they have interactive displays, places to try on costumes, so it is really fun for kids. Also, the gem and jewelry galleries are amazing as well. V&A has excellent free tours that last about and hour and bring many of the objects in the V&A to life. For example, there is a gown that I thought was sequins, but it actually turned out to be beetles. If you want to take a break, you can have a very nice lunch in the cafe.
- Natural History Museum: since you are in the area, it is next door to the V&A and it is a wonderful museum for both adults and kids. I know you are going to the Paradox museum (which is fun and very Instagramable), but if you have an hour in your schedule, it is a good place to stop for a visit.
- Restaurants near V&A. I like the V&A cafe, but it can get crowded. Since you are just across the street from the South Kensington tube stop, you will find a wide-range of options to get a quick bite to eat and then you can jump on the tube and head to the Knightsbridge station (Piccadilly line) and then its a few minutes walk to the museum.
Saturday: the itinerary is very doable, but it may be a lot to have two museums and then you have a show at 7:00 p.m. I would take a look at when you plan to eat and where and make sure you are not too rushed so that you can enjoy the show.
Sunday. If you are talking about visiting Westminster Abbey, it is not open for tours on Sundays. You are welcome to attend a service. Also if you are talking about the City, it is relatively quiet on Sundays. I know that London Walks has a tour that goes on Sunday afternoons. If you plan to take the RS walk (audio guide/guide book), then Sunday is probably not your best day to do that walk. We did it last week and it was fine. My husband was totally bored.
Monday. Tower of London is awesome. A morning where you see the crown jewels, take a beefeater tour, and visit the White Tower. They have really cool video games and activities in the White Tower. Also the Ravens are so much fun to visit, just don't bring food as they will chase to get at it. I have a great video of them chasing me for just a cough drop.
Sunday roasts: I have had two in London, one at the Hawksmoor in Covent Gardens. Food was good, especially the roast and gravy. The sides were okay and the environment was like eating in a food hall. This past week we had a Sunday roast at the Devonshire (they serve the roasts later in the afternoon as well, we ate about 3:30). This was amazing, from the house made rolls to the beef and all the sides were delicious. Reservations are so hard to come by, but I would go back.
Restaurants. Lots of options, if you can share the type of food you like, price ranges, I can make some recommendations.