I owned a 40,000 gallon in-ground pool and followed a method called the "Trouble-Free Pool method". The only chemical requirements are normal bleach (chlorine) and a pH adjuster. No "shock", no algaecide, no pool store shenanigans. My pool was pristine & sparkling blue, and never smelled or hurt guests' eyes or turned blonde hair green. My family (including two small children) could swim all day long and never have irritated eyes.

It's really about being very careful about the chemistry (step 1 is to get a high-quality testing kit). Public pools are... less than fastidious about chemical balance and standards are much looser.