Clean the surface to get any slime and loose dirt off. Use a primer that adheres to the type of material that the pool is made of, Killz or Zissner. Then apply the paint color in enough layers to the desired tone. Doing it right takes longer, but it'll last longer.

The paint in the pool would have stripped regardless without cleaning and priming which I'm guessing they skipped. The hydrogen peroxide just sped things up.

Read the manual, use the right product, do things properly, don’t be a lazy half-ass.

Prep, treatment, type of paint, and THIN coats.

Hiring experts wouldve been a good start...

Well, unless you're a large painting contractor with prior experience doing similar projects (something that's typically considered during the bid process), you should never be in a position to fuck something like this up.

But also, it seems like you care about the quality of your work, so you if you ended up out of your depth, you would have hired proper subcontractor(s) who are experts on this type of thing. You would also be actively communicating with the design engineers who approved the plans and specs to get clarification regarding materials, paints, etc. so if this did end up happening, you'd have a paper trail showing that you did everything in your power to prevent something like this.