[M_Six]

Assuming your pool house is electrically wired to your main house, just use powerline Ethernet adapters. Plug one in wherever your main router/modem is and plug in the other end to the pool house, then run an Ethernet cable from that to an AP, like an Apple base station or Google wifi. I have a webcam in our shed that runs through Ethernet-over-powerline and the connection is rock solid.

Modem/router in main house => Ethernet-Over-Powerline => 2nd Ethernet-Over-Powerline in pool house => Wifi AP (Apple or Google wifi).