While I do agree that the house rules apply, I've gotta say that as a parent of a 21yr old who lives with me, what he does when he is away from the house is his business, but the minute it comes into MY house it is MY business. Translate that into -- if a small package arrives in 9 months, or medication bills I will be demanding that my child take FULL responsibility for it. And my kids know I don't fool around with that.
Move this to the OPs situation - whether you chose to have sex with your boyfriend of a month or not is ultimately your decision and a motel room is not the only place to do this. Are your parents na´ve or, as I think, just trying to impress upon you the potential for long term consequences?
You could offer to pay for another motel room for yourself. Or get joining rooms. Or a room with two beds. Options -- always leave options open!
Without knowing your boyfriend and just generalizing - you can bet that sex will be on the ask-list. He'll pull every card because he'll be soooo sad without out and it will give him something to remember you by. (pile of BS, if you ask me.) But if you go, you'd better be prepared with your answer and be firm with your choices, including protection if that's in the cards. And think about it -- if he's gonna be gone, and you can both wait all those months in between, well, you can both wait now too. Not saying you have to, or should... just another perspective.
Do your parents have the right to say "don't go?" Yes. Should they? Well, not in my opinion if you are a responsible, capable adult.