Powering through London

To get a good overview you could take the HOHO bus. This will allow you to 'see' most everything as well as get off the bus when there is something of interest. Try to arrange the Tower for the least busy time (not sure when this is) then see what you can in the time you have. Windsor Castle will definitely take up some time, but if it is a priority then make it happen. It is a totally enjoyable place to visit... it's all about choices:)

I would probably skip Windsor just due to the time demand. The HOHO bus is a good idea, if I had to pick a site not mentioned, it would be the British Museum, it is free, and certainly one of the best ones out there if you are interested in Greek, Assyrian, and Egyptian culture.

I'd do the tower first thing (get there before opening), then some combination of the following:
-walking tour like the one in RS guidebook that goes by Buckingham, St. James and Green Parks, Trafalger Sq, Big Ben, a view of the Thames, and Westminister Cathedral. This is kind of a brief overview of iconic London.
OR
-a visit to the British Museum. It's free, and IMO a must-do. Then off to a walk or other site
OR
-a walk in the city - the old neighborhood near the Tower, and a visit to St. Paul's. I'm sure there are plenty of routes described online. From St. Paul's, walk across the Millennium Bridge. And pop into the Tate Modern, if anyone has even a passing interest in modern art. Free and the structure itself is worth a visit.

In any case, you should have time for an evening ride of the London Eye (reserve ahead)

There are plenty of other options…Greenwich, an afternoon at the museums near Kensington Park and the park itself, or even heading out to Windsor. But I really think staying in some combination of the major sites I've listed would be ideal for a first visit/first visit in 30 years.

I'll echo some of what's already been suggested with a few additions. Are you counting the day that you'll be arriving in London from a long flight as part of your 1.5 days? If so, factor fatigue into your calculations.

I would have recommended the Tower of London even if you didn't already have it on your list. It will take about 1/2 day.

Focus your remaining time on a few must sees. Unfortunately this does not include Windsor. Windsor is nice, but you are already seeing a castle (the Tower). Plus, it will take nearly a full day to travel and see it. Time you do not have.

Here are some options of top sites:
Big Ben/Parliament and Westminster Abbey. They are right next to each other. The Abbey often has a fairly long line, but there is a cash line that moves a little bit faster. This will take several hours. If you time this right you may have time to see the changing of the guard at Horse Guards before or after. It is nearby and not crowded. The Churchill War rooms are also in this area if you have an interest in World War 2 or Churchill. They take an hour or two.

London Eye. This will give you a nice view of the city. It has longer hours than some of the other sites. It is a short walk from Big Ben. Allow an hour or more depending on the line.

British Museum. You could spend a long time here. It's free so if you have even a small amount of time bungee in to see the Elgin Marbles, Rosetta stone and some of the other marquee Egyption and Near East holdings.

Hop on hop off bus to see highlights around town. Pick one with a live guide. This is a good option if you're tired, but you want to to do something the day you arrive.

Have fun!

Agree with Rob. Be certain to factor in the jet lag into your short visit. Also agree that besides a visit to the Tower, start your full day in Parliament Square (take the tube to Westminster Station). View Big Ben and Parliament, visit Westminster Abbey, then stroll up Birdcage walk through St. James Park to the Palace. Follow the Mall over to Trafalgar Square. Depending on time of day lunch in the crypt of St Martin of the Fields is nice. From there walk or tube up to Leicester square and then over to Covent Garden. Or if you are a big shopper, tube to Piccadilly Circus instead, maneuver through the crowds and head on up Regent street to Oxford Circus. Lots can be see in a day. Merely have to pace yourself and make good use of the tube.
You'll love London!

You said your father in law wants to see Windsor Castle, so he may want to leave the group and go do that one day when you are doing something that doesn't interest him, say, shopping. It's a very easy trip out on the train. If he expects that he will never make another trip to London, he should definitely do this.

These are all terrific ideas! Thanks for all the input. I think I've talked the group out of Windsor at the very least. Now just to pick the highlights from all the good ideas...