If you're very sure logic won't work on them and that they will keep harassing you if you don't quit your job/break up w the boyfriend (or may try to get you fired anyway), you have two options, unless you would want to try and move out, which can blow up your life:

- Tell them you'll break up with the boyfriend and then carefully lie to them (erase text messages, only see him when you know they won't track it, etc.). During this time, save up if you can to move out when you turn 18 or when you can. Lying is bad, yes, but it might be the easiest path for both you and your parents and this way you can have some financial independence and provide for the dog.

- Try to compromise and stop being sexually active with your boyfriend, allow them full transparency in your life and, in exchange, get to keep your job and maybe get to keep seeing him. Save your money and figure out how you can move out soon in the meantime.

Keeping your job is key as it will allow you some financial independence and more flexibility on coming going (not to mention your dog is taken care of).