I agree with the sentiments of most of the other posters:
This is a social issue, not an in-game issue. Dealing with it in-game and hoping it resolves itself that way is a capitally bad idea.

If talking to your family doesn't work, then you'll have to uninvite them. I'd recommend apologizing for the fact that the game isn't working out, and explaining that you're still willing to play Rock Band and Halo 3 or whatever with them, but that it's too difficult to play D&D with them around.