I got my 42123 a month or so ago and while it's a very awesome set out of the boy I knew I had to give it a proper differential.
Here's how I did it in LDD:
In order to preserve the original engine position the differential is moved back one stud:
A pair of 8 tooth gears transfer the power from wheels to the differential:
And while I was at it, I also made the steering work using 8 and 24 tooth gears:
I plan to make a detailed HOW:TO video tomorrow, so stay tuned.
Meanwhile you can download the LDD here:
https://bricksafe.com/files/Zblj/42123-differential-and-working-steering-wheel-mod/42123 Differential and Working Steering Wheel MOD.lxf