I seem to be a lone voice on this one, so maybe it's a cultural thing. Are any of the other replies from the UK?
Deep breath, I think both OP and her relative were wrong when they were acting as host; surely a gracious host would allow the guest to choose what they watched, or at the very least put it to them in the terms of "I'd really like to watch this episode of my serial between 8 and 9, but if there's anything you'd like to see at any other time, or if you'd prefer to have the radio, or music or nothing at all, please say.
However, having been put in that position as the guest first I can see why OP stuck to her guns when the tables were turned. The relative is pretty clueless that she thinks it OK to watch TV and ignore her guest, but when as a guest she spoke up to say can we watch ....., perhaps that indicates she thought that OP would have done the same if she'd minded one way or the other.
Now, that would have been interesting. If OP as guest had said, could we watch something else as I really hate this channel, this presenter, this programme and the relative had said sorry, it's my television, my choice. Then OP would have been really justified to take her stance, but would relative have been thick skinned enough to ask.
Don't really understand though why you'd have a visitor and then want to watch TV or a DVD. For example, if there's an important episode of a serial, unless you both want to watch it, can't you record it or watch it later via the computer? Nearly all our programmes are available for a week. The only time I can think that the television goes on when I'm visiting or hosting is occasionally to watch the news, we're too busy talking and crafting and catching up the rest of the time.