I think it's great he invited you out again, and you accepted. It is certainly better from the DB-ing POV for you to accept his invite than vice versa.
However, I perhaps would have avoided the "Why do you only invite me to family dinners?" question until *at least* after the first family dinner. You see, at this point, he has said he's not ready for something else/new with you, so therein lies the answer to that question.
With that said, though, it seems you both recovered nicely and now you have a lunch/dinner lined up, which is great.. just make sure you do your very best PMA-ing at the lunch/dinner and maybe avoid R talk altogether.
