"Very difficult and rare algae"?! I'm sorry, but you have been "pool store'd", as we say. They are basically saying "Sorry...we don't know our ass from a hole in ground...but please keep buying our expensive chemicals".
As stated earlier, if either of your would like real answers, using your test kit, please post a full set of numbers. Then we can give real advice that will result in a crystal clear pool.
OR....we can guess! My guess is that you need to SHOCK with a LOT of liquid chlorine to kill your algae bloom and overcome your high levels of CYA. Run your pump/filter 24/7 along with shock levels of chlorine until clear. But...thats just a guess without numbers. You could have high TA. Or out of control ph. Or crazy calcium levels.
Your water analysis will tell the tale.