Welcome to TFP !!!!
Why don't you post the test results from the pool store and we can look at that.
As a general rule we are suspicious of pool store recommendations. We generally advise doing your own testing and avoiding the pool store.
Cloudy water is not caused by low calcium. Its caused by organic matter or something else suspended in the pool. Like algae.
Test results would help.
We would recommend purchasing calcum chloride deicer at Home Depot or Lowes. Calcium hardness can be raised with calcium chloride or calcium chloride dihydrate. They are available in some areas as Peladow, Dowflake, Tetra Flake, or Tetra 94, often sold as a deicer by hardware stores, and some big box stores, in colder climates. Pool stores will carry either calcium chloride or calcium chloride dihydrate under a variety of names, including Hardness Plus, Balance Pak 300, Calcium Hardness Increaser, etc. Calcium products should be spread across the surface of the deep end of the pool.
But post the test results first i have my doubts you need it.
Backwashing and deep cleaning the filter help. Changing the sand is just a way to get you to purchase expensive sand. Its just sand. Here is a great thread on deep cleaning your sand filter:
Deep Cleaning a Sand Filter
There are alternative mediums to sand. But to tell the truth of the thousands of post Ive read and responded to on here -- I can't tell you it makes a difference.
UV --- It has its place but probably wont reduce your chlorine exposure over the long run. Why because you need to keep the same amount of chlorine in the pool to sanitize whether there is a UV system in place or not. UV only deals with the water that passes through it. Therefore the rest of the pool must be kept at minimum sanitation levels because the UV is not working there.
Also the sun does a great job providing your pool with high levels of UV. That's what is actually doing most of the UV work on organics in your pool the UV from the Sun. High bather load in the pool, indoor pool yes both probably need UV. Ordinary residential pool, doubt its going to make much difference.
Post some test results and lets look at your calcium hardness issue.