In England and Scotland for 3 weeks

If you haven't been to Hampton Court, just southwest of London, that should definitely go on your list of Tudor sites. Another candidate might be Montecute House in Somerset, built in the last years of the Tudor era but used to film parts of Wolf Hall. A search for "Tudor" on the National Trust website produces dozens of entries, so you could do some digging around there. I don't know whether Brighton and York are the best bases but your idea of using just a few is a good one.

I have been to Hampton Court. Have been each time I have been to London. It is beautiful. I will probably take my family there as it is an easy trip out of London.

Are you more interested in the city or the countryside? How strenuous is your ideal day? How much time would you fancy staying in one city/area? Will you be driving or using public transport? What is the maximum length of time you would like to spend travelling from destination to destination? You've got three weeks, are you going to split your trip evenly between England and Scotland, or is there more you want to see in one of those places?

These are some questions to help you logistically narrow down your options. Sometimes that's the only way to really get to the heart of what you want from a holiday.
Hope this helps

All the questions Samuel asked are important. The answers will help you narrow down your plans.

You're right that there are so many options! Three weeks may seem like a long time, but your schedule will get filled up quickly. Your built-in dates are when your niece is performing and when she and your sister want to go to London, so you can start by blocking those in on your calendar. It will be important to get answers from them to the "Samuel" questions, too.

Frankly, the south of England around Brighton wouldn't be my first choice. There's a wealth of choices en route between Edinburgh and London. I wouldn't see a need to go out of the way (at least not so far as the south coast), but others may disagree.

Samuel's questions have helped. I am thinking that besides London and Edinburgh I want to stay 4 days in each place. My plan would be two cities outside of the big cities. Public transit is going to be my mode of transit. I have no desire to drive in the UK because I don't think I am skilled enough to drive on the other side of the road or on the smaller roads that are in some of the more rural areas.

A big part of wanting to go the south of London is the Mary Rose ship, and the battle of Hastings. I chose Brighton because it is in the middle of the two which gives me a base. Wales was on my list but man the public transit and getting around to the castles and places I want to go is hard, so I am thinking that will be it's own trip at some point.

when is the trip katsrad?

For Tudor, do you know of Little Moreton Hall? https://www.nationaltrust.org.uk/little-moreton-hall

Older than Tudor, but quite relevant, do you know of Westminster Hall, the only remaining fragment of the Westminster Palace? Quite impressive.

Sorry! I thought I said, my trip is late June, early July. I have been to Westminster Hall but not Little Moreton Hall. I will look at that! Thank you.