I know I've been away for a while but maybe I can help.
While it's certainly possible to mix and match using di-chlor, tri-chlor and Cal-hypo safely, I think it's a bit too confusing to be practical. Pick one and work with it.

If you want to add Di-chlor, expect it will help with CYA (as Dave describes) but plan on adding calcium and muriatic acid and baking soda. Di-chlor isn't nearly as acidic as Tri-chlor.

If you want to add cal-hypo, expect it will help with calcium levels, but you'll need to add stabilizer, muriatic acid, and baking soda again. Cal-hypo isn't acidic at all

If you want to add Tri-chlor, it will work differently in that it is an eroding tablet. I like to use two floaters loaded with tabs when I am using it. This will be very acidic, will add CYA, albeit more slowly, and provide a more constant level of FC as it erodes. You'll still need to add calcium, and baking soda. You may also need to get to your maintenance level of chlorine using bleach. But this can be a painless way to three things at once.

Finally, you can do it all by adding bleach/Liquid Chlorine (my favorite), Calcium, Muriatic Acid, Stabilizer, and Baking Soda. Having a vinyl pool I don't add calcium, but I have used Cal-Hypo and don't care for how long it takes to dissolve.

A week ago I just got back from being out of the country for a month and returned to a pump our house-sitter had blown up, and a general mess. Over a foot of water had been lost (nearly 5k gallons). FC was down, pH was up, CYA was down, Alk up, salt level down. I added 120# of salt, one gallon of 12% LC, 4lbs of CYA, and about a pint of Muriatic Acid. Now the FC is around 6, CYA is 60, pH is 7.4, and salt level is an ideal 3000ppm.

But it's raining so we can't use the pool now!