North west facing garden
west central Scotland
Oh - the grass will be terrible, make no mistake about that. It will never be a thing of beauty in our climate here
Children don't stay small forever though.
It's a place where beautiful isn't enough of a word....
It might cost a fair bit, but removing the railings and building another middle terrace is an option. You would then have the middle and back terraces for 'grown up' things, and the area near the house for the children.
edited November 2020
My back garden is North facing, and since I have become personally responsible for it I have started spotting where the sun is when shining from the side in winter in this patch where the house casts a shadow.
Suggest regular photos at different times of day to get an idea of where your shadows and limited sun will be at different times and seasons, to inform planting etc in the future.
“Rivers know this ... we will get there in the end.”