I can certainly understand how it would feel awkward, but I can assure you this wouldn’t be the first or last time it has happened.
When I last visited (March, I think), as I waited to check into my room, there was a large group (~10 or so) occupying all of the center tables, eating and drinking. It’s not uncommon for groups of men and women to visit to eat, take a tour etc, so i didn’t think much of it. Then a young man (probably early 20s) emerged from the back with a beautiful woman on his arm, looking well ravished, and sporting a huge grin on his face…the group broke out into a cheer, and there were high-5s and congrats all around.
I surmised this was his first time, and that his friends and family had decided to be there to encourage and support him. It was strange (I could not imagine my own family doing some such thing!), but also very sweet in a way. Who wouldn’t want their first experience to be with a highly skilled knockout, and then be treated to a hero’s welcome by those closest to you, along with a few shots afterward?!?!
I would say that unless you are terribly embarrassed by it, let them come along. It sounds like your parents aren’t too judgmental, but are mostly concerned that you will be safe, and treated well. You will be. I’ll bet it would set mom’s mind at ease if she were to meet your date before hand as well (if she’s comfortable with that.)…She’ll quickly see that the women there are especially amazing and caring.
The room idea isn’t bad, as well, but your parents can pass also the time, taking a tour themselves, sitting out by the pool, having a meal or a few drinks in the bar, or heading into Pahrump to one of the nearby casinos, movies, bowling etc.
Feel blessed that you have such supportive parents!