What software do you recommend that will enable me to use English VTT files as the source to translate other languages into VTT files for subtitles? Ex. Existing English VTT files to exporting new Chinese Translated VTT files?
Are you asking about software that translates the files for you? If so I wouldn't recommend using software translating anything. It's never really accurate.
My recommendation for translation would be to find someone on fiver or another freelance website do that kind of work. Make sure they are familiar with the VTT file format, they are proficient in the language or languages you want them to translate to. Also make sure they are proficient in the English language as well.
If you want further advice for where to find people like this, please, feel free to reach out.
Best of luck!