My parents or my partner, which one, please help?

This is nothing but emotional blackmail. You will have to explain to them flat out that these are your terms and you are not prepared to give up your life to mind them. They can take it or leave it. If they carry through on their threat then you will probably have legal recourse which you may want to inquire about now. I would just concentrate on your successful relationship. He is not going to forsake you! Live in the present moment. No one can predict the future.