Someone else can correct me if I'm wrong but I don't believe they meant an actual fan, I believe they meant an aquarium cooling fan like
this, which can be purchased online and attached to the tank. The air moving over the surface of the water wicks away heat as it rises from the bottom of the tank to the top of the tank. Ones like that are in the $15-20 range.
If your parents are worried about dirtying water bottles for animal use, perhaps you could purchase a couple of dedicated ice packs (you can get ones at walmart or something for just a few bucks, the kind you would put into a cloth lunchbox), and you can place those into a plastic bag before putting them into the freezer so they don't touch anything else directly. You could also, if they would accept it better, possibly cool some clean, treated water in the fridge in a jar or a pitcher for water changes, or get a dedicated ice tray to freeze a bit of tank water (again, you could place the tray into a gallon freezer bag to prevent it from touching anything else directly). It's certainly not ideal, but sometimes you have to work with what you've got. Someone with more experience may be able to weigh in about the pros and cons of any of the above.
I don't know if anyone's ever tried it for this purpose, but in an incubator (like for birds) we use glass jars of water placed in the bottom to hold the temp inside the incubator if the power goes out. We keep them in all the time just in case, because they stay the same temp and the water in the jars cools off much slower than the air in the incubator does, so they radiate heat for a while longer. Is there a reason that this same theory wouldn't apply to a large, smooth stone used as a heat sink of sorts, if you fridged it or froze it and then placed it in the tank? sort of like a non-melty ice cube? The only objection I can think is if she lays on it, it might have the same potential for problems that a reptile heat stone would have, but if it was fridge temp rather than freezing temp I don't think it would pose a threat, and a stone can be placed in a sealable tupperware type plastic container to prevent the stone from touching anything.
Re: the blinds- perhaps you can tape cardboard to the sides of the tank that face the window. It's not the most amazing insulator, but it's easier to find/less obvious than styrofoam, it will make it darker, and keep the sun from warming the tank as easily even when the blinds are open.
Last resort measure, is there anyone you could take Tulip to for the summer that would babysit her until you're out of the house again and can take appropriate care of her?