How long should I spend my time...

First, I recommend investing in the RS guidebook as it will tell you much more than comments on this forum.

Do you have the option to fly "open jaw" (arrive London, depart Scotland or the other way around)? That will save you time traipsing north and back south again. Looks like you'll be concentrating on 2 or 3 limited areas: London / Oxford, the Northeast of England, and Scotland (see below).

There's so much to see & do in London I won't even start. And I've never been to Oxford, Manchester, or Blackpool. Near Blackpool is Lancaster (lovely inn along the canal is The Mill at Conder Green), and further south (en route from London) you could stop at Stratford-on-Avon and/or Warwick Castle.

I visited Liverpool for the Beatles Experience, Magical Mystery Tour bus, and Hard Day's Night Hotel (just for tea, we didn't stay the night there). Recommended for sure!

To get a taste of Scotland, since you'll be on the western side of Great Britain, I can highly recommend Inveraray (Castle, historic jail, horseback riding at Argyll Adventure, and the Auchindrain Township open-air museum) and Kilmartin Glen. You could also stop along Loch Lomond -- the Duck Bay restaurant is only about 1 hour outside of Glasgow, good food and a fabulous view of the loch. Your nearest major airport would be Glasgow, but Edinburgh is only about another 1 1/2 hour drive from there.

You said your parents love museums. In London, go to The British Museum, and The Victoria And Albert Museum. These museums have a great variety of exhibits, so there will be something of interest for everyone. Spend two complete days at the British Museum. (One if you are short on time.) Spend one day, or at least half a day, at the Victoria And Albert. Both museums have cafes, so you can have lunch there, and then continue seeing the exhibits.

You may enjoy the Tower Of London. Used in ancient times as a royal palace and a prison.

You may enjoy Westminster Abbey if you or your parents are interested in cathedrals.

You said you and your sister will be looking for something fun to do. You may like The London Eye, which gives you a birds-eye view of London. You may enjoy a boat ride on the river. The entire family may enjoy a ride on the Tour Bus that goes by all the most famous tourist sights in London. There is a host, or narrator, telling you what the sight is that you are passing by, and its history.

A good way to get a quick view around London is to take one of the Hop-On-Hop-Off bus tours. One of the companies that does it best is the Original Tour. They go by all the "must see" sights of London. And you can hop off anytime you want, look around a sight, then get back on the next hop-on bus that comes by. The tickets are good for 24 hours.
https://www.theoriginaltour.com/p/tickets/the-original-tour/

I would use the hop-on-hop-off bus as a way to give you a tour around the city, but regular red double-decker buses are the way to go for just traveling around London every day. In addition to the tube, that is.

That's just a start....there's so much to see in London! Hope this helps!

Be aware touring in November that the days are short. It will get dark around 4 or 5 PM, so outdoor sightseeing should be done early in the day.

Being from Malaysia you're probably not used to cold weather. It will be cold, so bring warm clothing or plan to shop for warm garments on your first day. You'll also need rain gear. London has second-hand shops where you can pick up what you need for less money than new clothes would cost.

See << http://www.timeout.com/london/shopping/londons-ten-best-thrift-stores >>

and << http://www.brokeinlondon.com/second-hand-shopping-in-london/ >>

Thank you everyone! Will definitely take the suggestions into consideration when planning for our itinerary. We will travel by car mostly. By the way any suggestions for shopping places?

It would depend on what you are shopping for and where you will be when you shop.

I hope you will not have your car in London. That would be a mistake.

Also be aware that the network of trains and buses in England will get you most everywhere you want to go. The exception would be remote places in the countryside.

What type of shopping will you be looking for? There are many luxury shops in London, but also very nice outlet malls in several locations in England. Burberry is one store I visited at an outlet mall outside of London, and picked up a great raincoat for one-third the price it would have been at a department store.

Do you want luxury items? Such as expensive purses?

Will you be buying, or just looking? For just looking, you may want to walk around Harrods store in London. If you are in the mood to buy a luxury item, they will have anything your heart desires there. Confession: I bought a purse there one time. Don't tell my husband!

You may enjoy the Bicester Village Designer Shopping Outlet Mall in Oxfordshire. 160 designer outlet stores. 60% off retail.
https://www.bicestervillage.com/en/home/
Getting there:
https://www.bicestervillage.com/en/getting-here/

You might want to use train & bus transportation until you get to Liverpool or Manchester, then rent a car from there. Or wait until you're ready to leave London and then begin renting a car.

It will definitely be easier to enjoy Blackpool and Scotland (assuming you want to see the countryside) with the flexibility of a car. With 4 people in your family, the cost for a car should work out to your advantage versus the cost of train tickets.