Should i invite my crush to family barbecue?

I'm 13 and all of my family is coming from louisiana and we're having a huge barbecue and my parents said i could invite some friends. i want to invite the guy i like, and the other two girls that we hang out with. we all 3 like him (it gets awkward at times), so i don't know who i should invite. i can't invite one of the girls cause she's grounded and my other friend always tries to show me up when we're around our crush. for example, on the last day of school he was flirting with me a lot and so she started acting all depressed and crying about how she's going to miss him so much (because she's going to high school next year). Should i invite both of them, or just him?