Are you talking about negotiating with your parents? If they told you their budget is ~$15-20k/year, I wouldn’t expect a lot more than that.
Leaving a private high school undoubtedly saved them money, but it doesn’t mean it’s available for college. Comparing what they’re spending on your sister for college to what they want to spend on you is one thing; tallying up what they spent on each of you in high school is quite another. They didn’t force you to leave the private school, so unless you were both given the option to leave (with the understanding that the tuition money would be rolled over to college) it’s unfair to retroactively change the rules. Just because you “instruct(ed)” them to put the tuition in your college fund doesn’t mean they wanted to or could afford to do it.
It sounds to me like you’re willing to throw your sister under the bus to squeeze more money out of your parents. Whether or not she’s doing well, has decided on a major, or wants to attend law school really has nothing to do with you. That’s between her and your parents. Instead of trying to browbeat them into coughing up the money you feel you deserve, why don’t you find a program you can afford on what they feel they can spend? Your sister had a budget and didn’t get to go to her dream school because it wasn’t affordable. How is it fair, in your mind, that you should be able to disregard the budget and go wherever you want? In effect, they’d be taking the money they didn’t spend on her and giving it to you. If that happens, I don’t think it will end well.