Well, Dominic, I can speak and read Polish fluently with flying colors, the problem is just writing long essays.
Wish you had said that earlier, because it changes everything. It may be that your parents idea is not as harebrained as I first though, just that they are going about it a bit wrong.
First, the bad news. With your current grades and your current level of Polish, it is probably going to be very difficult to get into a serious Polish-language program at a top-notch Polish university like the University of Wrocław. And, if by some stroke of luck you did get accepted, it would be difficult to keep up even if you worked your butt off. The drop-out rate at Polish universities is extremely high, with about half of the students quitting after the first year, and only a third going on to finish their degree. Frankly, I don't have much confidence in you making the cut until you learn some better study habits and improve your Polish, and that's going to take time. But I do have confidence that you can do it if you apply yourself and work hard.
Now, the good news. Warsaw is an expensive place to live, and, in my opinion, not a very pleasant city. The pleasant cities are Kraków, Wrocław and Toruń. The cost of living is slightly lower in these cities than in Warsaw, and the quality of life is, again, in my opinion, a lot higher. You could consider spending a year in one of these cities studying "General Studies" with the primary aim of improving your work habits and Polish, and learning about life in Poland. It would be a "throw away" year as far as academic credit is concerned, but it will give you a chance to work hard and make up for any deficiencies you have. My guess is that, if you excel, you will be a much more attractive candidate to a serious Polish-language academic program, in Warsaw or elsewhere. And that you would be able to handle the coursework they throw your way.
There is another possibility, though, that would make this all a lot easier on your parents budget. That is to study at the branch of Uniwersytet Śląski in Cieszyn. The university is a serious state university, like the ones I mentioned above. It is much smaller, and, in contrast to most Polish universities is situated on a compact campus just outside one of the loveliest little towns in Poland. Cieszyn is located right on the Czech border, and has a charming Polish half and a vibrant Czech half. It may be a little isolated from the rest of Poland, but it is only ten or fifteen miles away from a very large and exciting Czech city, Ostrawa. You could always catch the bus to visit Kraków, too. It's just a couple of hours away. And there is an express train to Warsaw, the Wisła express, from the next Polish town, Goleszów, which is within biking, and even walking distance from the campus.
Living in Cieszyn is going to cost about half what it does in Warsaw. It ain't NYC, but it is a culturally vibrant pair of small towns that have a lot to offer. And with Ostrawa within pi$$ing distance, and easy access to Kraków and Warsaw, you are not going to get bored before the year is up. Personally, I love Cieszyn, and spent at least two vacations a year there during my 12 years in Poland, and one year, I took four vacations there.
It has all the advantages of small town living, low cost and easy to get around, with none of the disadvantages, isolation and backwardness. The population is cosmopolitan and well educated on both sides of the border, and there is none of that peasant mentality you usually find in small towns.
I think taking a year in Cieszyn to do some acculturation and preparatory studies is more like what your parents would appreciate. It's much more realistic than enrolling in an low-quality English-language course, and it's a lot cheaper than Warsaw, Kraków and Wrocław, without having to sacrifice quality of life. In short, it is a better investment considering your present circumstances. Even if you do return to the States and do not get any academic credit recognized, which will probably be the case, it won't be a wasted year as you will return with better study habits and a better grasp of Polish, and the experience of living in "real" Poland instead of "fake" Warsaw. Talk this over with your parents.
Until then, read Polish voraciously to build your vocabulary, increase your reading speed and comprehension, and improve your sense of style.
The contact info for the university in Cieszyn is:
Uniwersytet Śląski w Katowicach
Wydział Etnologii i Nauk o Edukacji w Cieszynie
ul. Bielska 62
Best get moving on that now, as it will take some time to talk to the right people about putting together an appropriate one-year study plan for you.