Ok - as a Londoner I would say not to go to Madam Tussauds as is really overpriced for what it is - though you may have no choice if weather is awful or your son would make your life unbearable otherwise ) - it is hideously overpriced and the queues are always awful (I live over in North West London and am always astounded at the queues outside there everytime I pass). If you do have to do it, invest in a saver ticket which will get you on the London Eye, in the London Dungeon (apparently better than Madame Tussauds and suitably yucky to impress teenagers) and into Madame Tussauds without you having to remortgage your home...
Personally, would start off the day with walk along the river from Borough market to the London Eye (stopping off at Tate Modern along the way for abit of art and coffee) and then after the London Eye take the boat down to Greenwich which is beautiful and has loads to look at. Just go for the basic London Eye pre-booked flights.
Use another day to combine Westminster Abbey, 10 Downing Street, the Cathedral and a walk along to St Pauls (plenty of Starbucks to stop at along the way) - you can walk all the way to the top of St Pauls and the view up there is great (though is hard work on the legs).
Another day you could hit north london - Hampstead (pretty village on top of hill), Hampstead Heath (beautiful heath, with great views, outdoor swimming pools - complete with ducks), Highgate and Highgate cemetery (which is beautiful). If you've still got energy, you could also head down to Camden which am sure your teenage boys would like.
Really good show to go see with kids is the Lion King if you can get tickets - or maybe Wicked. Covent Garden - where lots of shows are near - is nice place to wander with lots of shops, bars, restaurants and entertainers.
Wembley is absolutely miles out from central london - you may wish to divide and conquer if your son really wants to go there .
If weather is not so great, British Museum is great. As is Natural History Museum and the Science Museum.
You should be able to cram most things in but really I think your day to day itinerary will probably be guided by the weather... hope you have a great time.