When is this for?
As you've already said 2 days IS too short for a trip like this from London.
Are you aware just how far it is and how long it will take you to get to Scotland? Does that estimate of 10 hours take in stops? You will definitley need them and this could easily add several extra hours to that estimate. That is not a one day drive, especially with a 6 year old.
Driving in the UK is slow and it will take a lot longer to cover distances than you might expect. Also motorway driving may be faster but is deadly boring with minimal views.....
Why Scotland? What are you hoping to achieve in such a short visit, or is it just a tick exercise for another country?
If you must go, then think about the Borders area which is less far to drive than Edinburgh and is relatively quiet as not many tourists visit there. What sort of things does the six year old like? There are beaches, or ruined castles to explore....
You don't say what other places you are visiting during the stay. Is it just London or are you seeing more of England?
To be honest, those two days could be much better spent somewhere closer to London. There's a lot of England waiting to be discovered and a lot of it is child friendly...