Itinerary for London

Do you love your father in law.. because this is a killer schedule for most folks.. but for an 82 yr old.. really?? My father is 80.. and STILL competes in Masters Tournements in polevaulting ( yes.. at an age some folks break their hips tripping on bathroom rugs, my dad runs down a path and throws himself in the air.. ) but he would never to such a run around. Its too much rush here and rush there.. not enough just enjoying what you are seeing.
Do you actually plan to see much of the insides of the museums.. because your schedule looks like you plan on just running in and out the doors..

We spent the whole day almost at the Imperial War Museum.. its that good . Its actually my fave museum in London now.. followed by the V@A.. both museums are best taken slowly.. an hour or two.. then stop for a café.. the cafeteria in the V@A is VERY special.. don't miss it.. the décor is beautiful. I think the kids will enjoy these museums.. especially the Imperial War Museum.

Some of the sights are just look from a distance to me.. like Big Ben and Tower Bridge etc.. same with Parliament buildings.. and even Buckingham palace.. just look at them as you go by on a bus or wander past them.

I didn't see the Tower of London on your list.. and really ,, it should be.. kids will enjoy it , the included tour by the Beefeaters is funny and informative.

I would skip Benjimins Franklin house.
I would skip

Day 2: (You've got two Day 2's? Not sure if the numbering got confused or you are deciding which plan to go for)
You might consider watching the Changing of the Queen's Life Guard at the Horse Guards Parade which is closer to the Churchill War Rooms than Buckingham Palace. Here's a link to the googlemap of the area. https://goo.gl/maps/MqTLl Here is the link to the Horse Guards. http://changing-guard.com/queens-life-guard.html

However, I don't think you are going to be able to do Westminster Abbey and get to any Guard changing at 11 as you will need to walk between the two. If the Abbey doesn't open until 930 and even if you just zoom thru in an hour you have the walk to the next venue. Walkit.com estimates the walk from Westminster Abbey to Buckingham Palace takes 15 minutes for a medium pace, 21 for a slow pace. It usually take me 20 minutes because I dawdle in this area especially along Birdcage Walk.

If it is your second choice for Day 2, I would pick Tower of London (you will see the Tower Bridge from there) and St Pauls and forget the rest.

Day 3: I would leave National Gallery until last and see how much energy you have. If you just want to run in and see, say, the Impressionists galleries, then that would probably work fine.

The schedule doesn't allow for any jet lag and even without this is a 6 or 7 day schedule crammed into half that so you need to cut it accordingly. You will know what your main interests are.

I would not use taxis - they are expensive, but use your Oyster cards on the buses. Easy access and you get to see some of London whilst you are travelling.

This may be a case of spending so much money on the London Pass with Transportation (generally regarded here as way overpriced and not many speak in its defence - sorry you didn't see the discussions here before you bought) that you feel that you need to see so much to get your money's worth out of the passes.

My strong advice would be to dial back and only do those things that you all really want to do and listen to your bodies telling you to stop, especially your father-in-law. You won't be able to do everything so choose a reasonable amount and be flexible.

I also don't see how you can do two Day 2s if you only have one Day 2 to work with.

I was there in March with 3 teenagers and wife. Walking through Hyde Park and Kensington is good for Day 1 as it will help with the jet lag. My teens loved watching the ducks and swans on the Serpentine.

On the whole your schedule is too packed. Pick out the things you want to see most in each area. Skip Changing of the Guard - it's just not that great for the time it takes in the middle of the day. Westminster Abbey is great. Churchill War Rooms is great. Prioritize. Your party will be worn out by 5:00 most likely. Save some energy for an evening musical or concert at the Royal Albert Hall.