I think that I'd put it as close to the fence as legally possibly ( for max yard space) & probably as close to the shed as you could deal with...
for storing chemicals & if you have electrical in the shed, you can put your pump in there.
This would also limit the tree debris in the pool.
I'd move the swing set to the other side( of the tree), so that I could keep a better eye on the kids swinging ( just-in-case they try dumb things, like kids always do...lol)
without the measurements of the yard, it's hard to guess on sizings
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