Best option for Museums/Travel in England?

Something to include in your thinking on this:
Unlike many European cities, in London the following (and more) major sights are free (small donations requested but not required):
National Gallery (art)
Victoria & Albert Museum - has everything not in the British Museum :)
Natural History Museum
British Museum (has everything)
British Library
Trafalgar Square (exterior)
National Portrait Gallery
Covent Garden (exterior)
Changing of the Guard (Buckingham Palace)
Tate Britain (art)
Tate Modern (art)
exploring these central area parks: Hyde Park, Kensington Gardens, Green Park, St. James Park, Regent's Park
and more

You have to look at what sites each pass covers in order to compare their value. Since many of London's top museums are free, the London Pass might only cover a couple of things you want to see. The Heritage pass covers historic homes, castles, abbeys, gardens, and Stonehenge; do you have several on you list? Train tickets between Brighton and London Victoria station cost 18 pounds roundtrip; your relatives will know all the tricks, or see www.nationalrail.co.uk.

Isn't the Oyster southern limit just below Croydon, not even as far as the M25 ?

The National Trust also do an Overseas Visitor Pass. If you are a member of the US Royal Oak Foundation you will have free entrance to all National Trust properties

http://www.royal-oak.org/

Plenty of NT properties in the area

http://www.nationaltrust.org.uk/visit/local-to-you/london-and-south-east/

While it is true, and significant, that the big museums in London tend to be free, they have lately taken to charging ten or more pounds for "special exhibitions". Those are usually mostly "loan" shows, so it doesn't affect your seeing their permanent collections. But if you have any interest in the specific exhibit, I don't believe there's even any kind of pass that will get around the special fee. Only a "member" of the museum escapes the fee.

When we were in London last month, the Tate Modern had two large visiting exhibitions, "Matisse Cut-Outs", and "Richard Hamilton". Each was 14 Pounds, separately. (Edit: NY Times says 18 Pounds, so I must remember wrong.)

You have not provided enough information for anyone to answer your last question. What day of the week are you arriving in London/Brighton, by what means of travel, and how many days until the day on which you depart the London area - by what means? It even makes a difference whether you arrive at Heathrow before 8AM, because the Tube fare goes down at 9:30AM on a business day.

Did you mean to say you are sleeping in the city of Brighton, on the English Channel?

The Oyster Card is NOT VALID to and in Brighton. Brighton is on the Sussex coast and is over 50 miles from London. Oyster Cards are only valid with the 6 Zones of urban and suburban London.

An alternative to a Day Return ticket from Brighton to London and Oyster Card for travel within London is a Travelcard from Brighton. That gives you one journey from Brighton to London and return, and all the Underground, Overground, red Bus and Croydon Tramlink you can use in a day.

It comes in two flavours, all day and off peak. With the much cheaper (and much less crowded as the London to Brighton line is one of the most crowded in the country) off peak one it is not valid at the peak morning and evening traveling times.

If you are considering the Heritage Pass and the National Trust/Royal Oak pass can I assume that you have access to a car? Most of the properties covered by them are quite remote as they tend to be country houses.