I watched The Lighthouse with my dad a few years ago and I think that was the most awkward movie watching situation I've been in. We decided to watch it because it had Willem Dafoe on it, a positive rating, and it was on a streaming service he had. It's not really a spoiler but the movie has multiple scenes with a focus on masturbation. Neither of us turned it off because we kept assuming that was the last of it and we would have had to get up for the remote.
I can relate. In my teens, I watched Monster's Ball with my dad and sister, and in around the same span of time I watched Mulholland Drive with my parents.
I’ve never seen Monster’s Ball, but Mulholland Drive was pretty hot. I’m sorry you had what should have been a wonderful experience marred by awkwardness.