I'm from England, so I don't know about schools in the United States but I think that your parents want you to go to schools in the UK as UK schools have stricter systems than the United States. In the UK most public schools require you to have a uniform, and there are stricter rules and the schools usually push their students to work to their full potential.
I don't know much about the US but the country is so massive, there's so many more schools there than the UK, the states are also governed differently from one another too unlike to UK where it relies on one system.
However, when I was in high school I had many Chinese friends and schools in the UK often go on trips to China now and then. I think it will be easier to learn the English verbally in England or other parts of the UK and as English is not your native tongue, I think that with your current accent it will suit to learning an English accent, learning an American accent isn't so relaxing on your tongue as an American accent requires a lot of emphasis.