Help! Help! New Improved Clorox

[waterbear]

The indgredient in the new Clorox is sodium polyacrylate, which is also the ingredient in some water clarifiers. It is not what is making the pool cloudy but it might be causing stuff in the water to clump so you filter will filter it out. If her pool is green then it will turn milky white as the algae dies and it can take up to a week for the filter to clear it again. What I suggest you get is a large bottle of "Pool Owner Patience" and apply it liberally to yourself and your sister-in law!
Give the filter time to do it's work once the algae is killed. It can sometimes take up to a week or two to clear a really green pool. What you are seeing is normal. It's just dead algae. Generic bleach is going to be cheaper than chlorox so use that instead. Just check the label for the concentration. Regular bleach will be 5.25% and ultra bleach will be 6%.
EDIT: be aware that some cheap generic bleaches are only 3% so you need to double the dose if that is what you get! Read the label before you buy it and try to get 5.25% regular or 6% ultra if possible.
Also check the price of liquid chlorine at the pool store. Sometimes it's actually cheaper than bleach. (It's the same thing but somtimes more concentrated). A pool store near me sells 12.5% (basically twice the strength of ultra bleach) in 2.5 gallon carboys for $3.99. You do have to pay a one time $5.99 charge for the carboy but after that refills are only $3.99. In my area that is a much better deal than bleach. The cheapest I can find 5 gallons of ultra bleach for (the equivalent amount) would be $11.25!