Vermiculture, or worming takes a lot of work and dedication. I don't care what anyone says, I have done it and I was amazed at the care needed to keep the blood mites out and the worms happy in all weather. Eventually I dumped my worms into my
compost pile and they have been happily turning waste to black gold for years.
What I would do is start a compost pile. Lay dry carbon sources down first, layer in the strained muck (use a pool net to scoop it out), layer on green matter, repeat. This will create a hot pile which will burn up any possible "bad things" that your wife has a problem with and eventually you can use the clean compost in all areas of your garden.
As for the thoughts on chlorine--it evaporates out via gassing over time and why you need to replace it regularly--if there were still chlorine IN that pool, it wouldn't be black, so that isn't a problem.
Good luck!