I built and maintained swimming pools to get through college back in the 70's, both vinyl lined and concrete/plaster. That's when I learned how bad drinking water is to swim in. It simply doesn't have enough disinfectant (by design) to kill off things that are bad for people by skin contact, especially when exposed to air for any length of time. Most of the pools we built were filled with city water, and nearly all of them took 50+ pounds of chemicals to get them treated to safe swimming levels. Don't even ask about well water. I HATED treating one filled with a well. It took weeks to get it clean with daily treatments and vacuuming. Worst part was topping off with the same water that had the problems to begin with. Guess what just happened to all the hard work? Actually, 3.0 ppm is pretty close to what's needed for pool water, and shocking a pool will take it up around 6.0 ppm. Shocking is exactly what it sounds like. It gives a chemical shock to all the little bio-creepies in the pool. Pool water isn't for drinking. PERIOD. For pool water to be nice and clear, it takes a LOT of chemicals that you'd probably rather not ingest. Kids don't care about getting pool water in their mouths, so it needs to be a lot safer than drinking water, ergo, the elevated chlorine levels. It needs to be as close as possible to a neutral 7.0 pH. If the total alkalinity is too low, then it will dry the skin pretty bad. Lotsa tweaking to do to pool water. It ain't just about killin' bio-baddies.
Based on the photo, it's a pretty small pool, so it may be cheaper to replace the water than to treat it, especially if you need to water your garden anyway. The cut-off is around 5000 gallons before chemically treating is more feasible than replacing the water. If you just want a little boost on disinfectant after you refill it, yeah, go ahead and dump a little bleach in it. Not much though. Bleach will raise the pH pretty quickly. Bad for the skin and eyes, and won't supply nearly as much chlorine as you hoped. Figure out how much (based on the pool volume) to get it to around 1.5 ppm - 3.0 ppm, and then dose it slowly to raise the chlorine levels. The smarter idea if you want that bump to last a little longer is to buy a box of stabilized chlorine tablets and use those.
Fact of the matter is that I wouldn't get in a little pool like that (no circulation, no filter, no chemical system) if the water was more than a couple days old. A human body is one of the nastiest things you can put in water, and rain is nastier than a human. This is why bathtubs have drains, not because we use soap in 'em. Water the lawn, forget the chemicals. If you're gonna have to water anyway, why would you spray the grass with clean tap water and try to clean up dirty pool water? You had the right idea to drain it and replace the water. I'd be doing it at least once a week, if not twice. If you must, clean the pool (while it's empty) with a stronger bleach solution, then fill it up. You're better off not putting chemicals in one that doesn't have built-in circulation and filtering, other than some algaecide. A bottle of algaecide will probably last you all summer in that little pool.
