Need help with Backyard WIFI setup

Hello friends. I have a 3500sq ft home that is on top of a small ridge and have a pool house that is roughly 100 yards down in a small valley. The entire property is roughly 1 acre.
I have been scouring info on AP's and Extenders from all brands like what Amped offers and Ubiquiti and Engenious as well. The Kicker is I just have a Lan source at the very end of my home which is my office, but it is located on the back of the home and I could transmit from outside there. I could set up a High power AP that would have to transmit 100+ yards down to the pool area...trees inbetween are involved too. Im guessing I will need another device to comumicate with the kiddo's ipads and iphones due to the far range.
I also have a Gazebo halfway down to the pool area that has 110 power to it, but would have to involve an extender instead of an AP as I have no Lan there. And On top of that, the Gazebo may be too far to comunicate with my wireless router in my office.

I could do a non wireless Router and a Mega AP that would support the House and rest of the property or start breaking down multiple devices.

I just dont know which direction is best. Figured you guys here would know exactly which way to go.
Thx!!!!