Top 10 Sights for Diverse Family

I am not sure that Madame Tussaud's would appeal to the little one. Notting Hill is a nice neighborhood, but nothing exciting in particular. The Tower of London, the London Eye, the Imperial War Rooms or the British Museum would all be good. I'm not a spa person, so I can't recommend anything in that area, sorry. I think people underestimate how fun it can be just walking down the streets and seeing the shops and hearing the people. Or spend some time in Hyde Park or the zoo.

Honestly, when my kids were 3, their favorite part of London was riding the Tube. Everything else was just a tax to be paid before they could get on the subway again. (My oldest is turning 17, and still loves riding the Tube!) A little divide and conquer can work well. There's no reason you all have to do everything together. e.g. Mom takes 3 y/o on the train to Bath. Train ride-fun! Swimming-fun! Playing in the water-fun! Drinking stinky water-eewww! Dad and 18 y/o visit London museums-cool! In London, everyone can ride the London Eye, then divide up for little kid park time and big kid theater time. (Holland Park and Kensington Palace have fabulous playgrounds!) The Imperial War Museums are a good idea because the large machines may hold some interest for the 3 y/o. The London Transport Museum in Covent Garden is a gem for toddlers and an older kid might like it, too. Or, you can let the older one prowl around Covent Garden on his (?) own while the others take in the museum. Counter-intuitively, Westminster Abbey is an excellent place for small kids to visit. They offer a scavenger hunt sheet that even small children can do (finding carved animals and such) and I recommend it highly. The docents are very kind and helpful to engaged kids. And of course, the depth of the history there is super for the older members of the family. Our youngest quite liked the British Museum when he was 4 (mummies!), but it may depend on the kid. Teach your little one as much as you can about Britain before you go. Knowing about things like double decker buses, Big Ben, castles and such lets them enjoy the excitement in spying these icons for the first time. We read our kids a child's history of Richard the Lionheart and they went crazy when they saw his statue in front of Parliament. Wow-that story was really real???!!

Well i think the British Natural Museum has enough for everyone to be interested.I would also assume that the older child( adult really) could have some freedom from you and do his/her own thing a bit. For instance start slow, meet in cafeteria at museum after two hours. She enjoys the exhibits she wishes, you entertain the three yr old with exhibits more her speed. Fat Tire bike tours , do a nice city tour, your 18 yr old could do that on her own easily. ( my nephew spent 10 days alone in London at 18 and he was a country mouse, raised in a rural area without even public buses, and he managed!)
Frankly I think you should plan on splittinng up now and then, wife does a spa , you take three yr old to park etc.

The Lion Statues at Trafalger Square are a favorite photo op for kids and teens, riding the Eye, riding the tube (non rush hours), walking along the canals, boat trip on the Thames to the Tower of London (if the weather is good), taking a train to Bath to explore the Roman Ruins. London's train stations are very interesting and I think would be eye openers for both of your children. Highgate cemetery is very intriguing. Need to reserve a spot to see it, the side where Karl Marx is buried. Watching a soccer or rugby match in the Hampstead Heath.
Horniman Museum, British Museum, Theatre Museum, Transport Museum. Loads to do.

Take the barge from Little Venice to Camden Markets. Go to Hamley's toy store on Regent Street, the London Zoo in Regent Park. Take a boat ride on the Thames - from Greenwich to Westminster or Westminster to Richmond and the train back.