Hi brazilmom,
I am not an expert I grew up with a inground vinyl pool similar in size to yours and still take care of it occasionally, we go over and help open and close it most years. We are about 5-10 miles away from Brookfield.
This year we opened the inground pool later in the year than normal it was green, then cloudy, and it would not clear up. This cloudy water also happened about 5-6 years ago after half a summer of fighting it, adding de, and slamming it the only thing that fixed it was changing the sand in the filter, all of it. So this year they also changed the sand after about a week and a half of cloudy water. It is now cleared up. I believe they used silica sand, which was harder to find, some pool stores in the area carry other types of pool sand but it has not worked as well over the years. You'd think sand is sand, but in this situation silica sand works best for this pool and they have had at least two different sand filters and a few different pool pumps over the years.
Just thought I'd agree with changing the sand. I did not do it either time it sounded labor intensive they used a shop vac, but it worked.
Our little above ground pool, 8000 gallons, just across town from the other pool opened clean we could see the bottom when I took the cover off. We opened both pools the same week. It is interesting what the pool store guy said it was the snow but who knows. We have a solid winter cover on our little above ground pool maybe that's what the difference is? The inground pool similar to yours has a mesh winter cover that lets the rain/snow in maybe the pool store guy is on to something?
Best of luck! Sounds like you are on the right track