Your parents sound like a nightmare, frankly, and a lot of the stuff you’ve come to think of as normal sounds borderline abusive to me. (Apologies for using such a loaded word. My perception may well be completely inaccurate, so please don’t take it as an accusation that you have to confirm or deny. I’m just saying that, to an outsider with different experiences, the level of control they exercise over your life seems quite alarming.)
Unfortunately, I forsee a lot of future conflict when the reality of you going away to school and living on your own hits them; those faultlines are only starting to appear now. But that’s a problem for another day, so let’s focus on what’s bothering you right now.
I expect that any attempt to explain your emotional response to their overbearing behaviour will be taken as you acting out or seeking confrontation rather than as initiating dialogue. One hack you may try, which won’t help them see things from your point of view but may get them to cooperate with you, is to tell them that you need to go to the cinema or hang out with friends from time to time in order to be more effective in your work. Don’t just promise you’ll work on applications all day on Sunday if you can see Black Panther on Saturday; say that you’ll work regardless of whether they allow you to go out because you understand how important it is to get into a good college, but if you go out you’ll probably be feeling more refreshed and inspired in your work because taking mental breaks helps you to refocus. Maybe that kind of argument will get through to them.
Re. the application process, you absolutely need to talk to them about money as soon as possible. Tell them that all their preparation will be in vain if they don’t have an accurate idea of how much money they can pay, and how much money schools will expect them to pay. This is true, and they need to understand it.
One other thing: How many times have you taken the SAT? Maybe this has changed since I was applying to college, but as far as I know colleges don’t like to see students retaking it more than twice.
Sounds like your school choice may be a major point of contention if you get into a school they like more than UMich, so start thinking about ways to sell them on UMich or Barnard or Carnegie Mellon now. Again, an idea to work with their logic instead of challenging it (which is not a healthy long-term strategy): Get an outside authority they respect to make the case for what you want. A private college counsellor, another parent from your community, etc. Use successful alums who studied computer science as career exemplars. I don’t know. This will be tough.
I’m really sorry you’re in this position! The most important thing I can tell you is that your frustration is absolutely valid and the way they’re treating you is unfair and controlling. The parents in this thread who are trying to make you see things from your parents’ perspective may be well intentioned, but they’re misguided. I’m pretty sure you understand your parents’ perspective, and I imagine knowing they care a lot doesn’t make their authoritarianism and seeming lack of interest in you as a person any easier to swallow.