One solution is to put a 4X4 " pressure-treated post in the ground at each side and attach the bracket mounts to it.Pretty sure your pool doesn't have the top vinyl ledges to install that type on.
Thank you for the suggestion!(I couldn't get the play button to work, but I found the link in the page source:)
As is mentioned in the video, the reel should be closer to the pool, but otherwise, it's perfect!
I would suggest a sliding piece of wood on the side of the 4X4 on the right to lock the handle.