I used to have a very small pool like this when my kids were little. I can steal hear their squeals of delight when they and their friends played in it, great memories!

All I ever did was to add 1/4 cup of bleach in the evenings and swished it around with a soft household broom. The pool didn't have a filter or a pump. When the water got muddy from little feet I dumped it and refilled it with the hose. The sun heated it up very quickly.