I agree with a PP's point (I believe that it was SamiHami) that the hosts clearly know how to send an invitation to someone when they want to, as evidenced by the fact that they managed to mail one to OP's father, but somehow they can't get a paper invitation sent to OP, or even an FB message? And the only word OP has that she is in fact invited is from her father, a previously proven unreliable source.
My own family is a bit like this and when family members, who sound like OP's dad are involved, there's a lot of "of course you're invited" or "of course X Y Z will happen" but not based on any facts, just because they will it to be that way. And the one who ends up being embarrassed by it is the gullible one who believed what that person declared.
On EHell, we never tell someone "call the host and see if you're invited"! If they wanted to invite her, they would have.
And I don't recall any other threads about OP and her father, but for every story of "My parent died young so you should really bend over backwards to cater to your aging parent" one of us could counter with "my parents suck and I spent most of my life slaving to please them at the expense of my own happiness and now I've wasted my life being an unhappy doormat" or another story of "Bob always gave up his free time to please his elderly parents and then Bob's life ended young tragically so he never enjoyed life."
My 2 cents is that OP is not a taxi service. Why add insult to injury and be a long-distance taxi service to not even attend a family event? If family is so important to OP's father, why isn't OP's father important to extended family? Why aren't they making sure he has a ride? Why isn't OP important enough to them to be invited (with or without her father)? Heck, why isn't OP's comfort and time valuable to her own father? He cares about what he wants to do and not about the fact that his child is being disrespected and not sent an invitation. Or about OP's freetime.
I say, you weren't invited. Let your father, who lives alone ask other family members for a ride. Or he can try to host a gathering himself in his own town (at a restaurant, if at home is too much work) and he can invite the same people to come see him, if he wants to see them so much.