Change seating for second class Rail Europe London to Edinburgh?

Our family of 4 is booked on Rail Europe from King's Cross to Edinburgh

Oh no you're not! Rail Europe is a travel agency who re-sells tickets outside Europe. They do not operate or own any trains.
The trains from London to Edinburgh are run by Virgin East coast: https://www.virgintrainseastcoast.com/
information about seat plans is here: https://www.virgintrainseastcoast.com/rail-travel/your-journey/seating/

You will not be able to switch seats at the station (London Kings Cross). The seats will have labels on them "Reserved Kings Cross to Edinburgh". Once the train has left Kings Cross, you can move to any seats were the passengers have not turned up ("no-shows"), or any unreserved seats.
Note, you need to know coach number (letter) AND seat number. There are seat numbers 72, 74, 52, and 38 in every coach.

Since you have bought your tickets through a re-seller, you need to contact them if you are not satisfied with your seat allocation.

Did you request aisle seats? That's one feature that I see in common between those seat numbers. If you entered all four passengers in the same booking request, the computer will normally try to seat you together.

Were you fairly late in booking your seats? Trains to Edinburgh can be super-busy in August. A lot of solo travellers who've booked earlier will have requested window seats. Families who've booked earlier will be allocated the smallish number of table seats. This will then leave a lot of aisle seats, and it sounds as if they've found you the four closest together that were available.

Additionally you booked via Rail Europe, which is a third party - I wonder if they even have access to the full range of seats.

You could just turn up and hope that some people don't take up their seats (this isn't unusual) and you might be able to move. Also often there's an unreserved carriage. Obviously this can be very busy as people without seat bookings try to grab good seats but if you're quick in boarding and run for it, you might get a group of seats together.

Davie, Check the receipt in your ticket packet. There should be a phone number for Rail Europe--they'll help you! I haven't used Rail Europe for at least 15 years but they were extremely helpful when I had a similar challenge.

Thinking about why August is so busy, as Emma and Jane reminded us, the Edinburgh International Festival, Fringe Festival, Royal Military Tatoo, August Bank Holiday, etc. are probably reason enough not to spend much time on the seat assignment question.