So he agreed to a movie and stay-over at your parents' house, but now wants to back out when you've already discussed it with your folks?
I can completely get why the two of them would be uncomfortable sleeping over at your parents' (there's no way I would even consider it myself) but your SOs did know you live with the parental units when they got involved with you, right? If that's news to him/them, that's one thing. But if it's been known all along, then did he/they think they could totally avoid interaction with your family? That would be an unrealistic expectation, IMO, and avoiding the meeting makes him/them look hinky.
But what's putting up the red flag for me is agreeing to the date, and now saying no. Did something change? Does he feel uncomfortable about meeting your ppl? Are there deeper issues here that need addressing? Or is he just unwilling to be inconvenienced and potentially have to forego sex for one night in order to make you happy and reassure your parents?
My advice to you, Sweet Sister, is to trust your gut. Find out what's really on with him/them, and then follow your heart.
Or else just go on the date night with your gf without him.