OP, different cultures have different expectations, as well as different families within those cultures. However, you will be a guest of your boyfriend’s parents, as it is their place and they will be on the premises. Explain to your parents that they have invited you and that you and your boyfriend will not be spending nights in the same room.
I do not think that would be scandal, nor providing an occasion of sin, nor would my family, back in the 40s and 50s, but some Protestant groups would have thought so, and, possibly, even some older generations of Catholics.
It would be providing yourselves with an occasion of sin, however, and scandal, if you go camping by yourselves. Let your parents get to know your near-fiance. You two try to spend a lot of time with them. Invite them to go with you for ice cream, to see the city skyline at night, play board games, sing karaoke in the living room, or everybody pick walnuts or pecans out of the shells and make fudge. Give your father and this man a chance to talk without other family present, or maybe go shoot pool or darts together.
Just give the three of them opportunity to learn to genuinely like and trust each other. Laying a healthy foundation for the relationship between your parents and fiance now is very important for a healthy in-law and grandparent relationship as the years pass.
Best wishes! Let us know how it goes!