I'm going to go against the grain, also, and defend the OP a bit here. I can more than understand her feeling irked about not receiving a direct invitation (even though it was claimed - through an unreliable third party), especially considering the embarrassment that occurred last time. I, too, would be reluctant to show up, trusting that I was invited, even though that might very well not be the case.
I'm especially irked on her behalf that the father of the new parents - who is facebook friends with the OP - can't even take two minutes to confirm that she's invited to attend. I think the idea of driving up there and acting as chauffeur is a good one on paper, but in reality it would be not only a huge inconvenience but downright hurtful. Not only that, but that's half a state away, if I know my geography. It's not like popping around the corner to drop him off for a couple of hours. This is a huge chunk of time and driving and gas money. I know gas ain't cheap up in New Jersey. I probably wouldn't feel terribly enthusiastic about any of the options - whether it be to suck it up and just drive him up there, or risk attending with him, knowing that I may very well not be welcome, or contacting the hosts or a family member to find out the status.
My father was like this too. He would assume things, and pass them on as fact, and if you took his word for it, you had a one-way ticket to Awkward City. I learned quickly not to take at face value anything he said, because he was so optimistic and didn't have an ounce of guile, that he naturally assumed his beloved children were welcome anywhere he was. Which was simply not the case at all. After a while, I learned to either confirm it for myself (awkward in itself, so not very often!) or just skip it with my regrets sent through him. Of course, he didn't rely on any of us for his transportation, so that wasn't an issue. But I can understand where the OP is coming from. I don't think it's stubbornness, really (well, maybe a tiny, little bit...but with good reason imho).
OP, I'm wondering, how would you handle things (or your Dad, for that matter) if you wanted/intended to drive him down there - but couldn't because you had to work or had other pressing obligations that you couldn't cancel? Would he simply not go? Would you try to make other arrangements?
I suppose one thing you could do, if you were so inclined, (and this is honestly how I would handle the situation; I just don't know if it's the eHell approved way to do it) would simply be very honest, and contact the friend of yours on facebook (probably by phone, if possible) and let him know really wants to attend, and could he help you figure out a way to get him down there (if you're not invited)? That way, if he says "oh, but you are invited" that takes care of that, and if you're not invited, you're not assuming and he's not extending it - then you can place the responsibility on your hosts to work out your father's travel arrangements - I mean, I think this is a little more subtle than calling up and saying "I haven't been invited!"
Would that work?