This is not, I predict, going to end well. If OP just tells her father she is not going and he is on his own, holy heck will break loose and OP will end up going at the last second, because "of course she was invited. Dad TOLD Uncle Bull so, twice!" If her father ends up not going, she'll never hear the end of it. "Of course she was invited...." She will never hear the end of it, either way.
Giving Uncle Bull a list of options isn't going to cut it, either. He will not do anything because he wants OP to drive him, come hell or high water. Also, it sounds like car services are not an option where they live, and even cabs might be impossible. Airport ride services from small towns are often independent and flexible. So are teenagers and college kids, many of whom would love to earn ten bucks an hour, a full tank of gas, and lunch money.
I think OP needs to make her father's transportation arrangements for her own sanity and not go herself, because she was not invited. Find a local young person to be his chauffeur for the day. It may be the beginning of a beautiful relationship -- at least until graduation.