Hi Brent;

1. Trichlor will work; you'll just need to switch to bleach or cal hypo with CYA gets higher.
2. If you have no heater and no SWCG, you can use cal hypo without a calcium problem *IF* the trichlor feeder is DOWNSTREAM of the filter.
3. Actually using cal hypo will work very well with hard water *IF* you do it in the manner I can explain. But, I want to make sure it's safe first. If you get cal hypo inside the feeder with the tabs, the feeder can explode.
4. Don't add stabilizer, if you are going to use trichlor.
5. Do NOT buy trichlor ANYWHERE but Sams Club ("PoolBrand" brand, only) or from Amazon, using my links. Once you've learned to decipher the chemical labels, you can look around, but most of the trichlor being sold is a hodge podge blend, often containing copper.
6. Once you get your routine established, you can probably manage your pool with cal hypo, trichlor, borax, and maybe a gallon of muriatic acid.