Posted: 26/02/2015 at 22:00
Kids + paddling pool = mudbath. If it's a regular feature then you'll need to be prepared to sacrifice a small area for a while. I'd get some tanalised wood from the builders merchants and create a square, lay membrane and put down play sand so the pool can sit on top.
As for the lawn, even though it's east facing it should get some sun.
Drainage must be an issue, so regular spiking and brushing in sharp sand will improve it. Use a grass seed for shade to reseed it and use a mixture of sharp sand and compost to sow the seed into.
Lifting the lawn each spring increases air in the soil which combats compaction (You push a fork into the grass and literally lift it till the surface cracks).
Over time it will improve, but it's hard work.