To answer a couple questions, culturally, this relative hasn't been raised to speak up or appropriately assert herself. Hence the worry that her father would be upset if she upset the doctor.
I can appreciate wondering why she'd ascribe motive to the neighbor. I'm not sure what others' areas are like, but ours is becoming pretty divisive around this issue and somehow it's become politicized. Based on how her neighbor is presenting and talking, I can understand how she'd come to that conclusion. He's actively stating he's not going to socially distance and is posting in a way that could reasonably lead one to the conclusion that he's intentionally instigating her.
I liked the perspective that people are speaking more to their neighbors and that's a nice, generous position. Personally, if someone hasn't spoken to me, ever, and then they get into my personal space (which is now a six foot radius), it's going to feel aggressive. Not neighborly. That's why I'm planning what I'm going to say now. Before it happens.
To the explanation giving. Personally, I'd like to not give one and use "I'm keeping my distance." (Thanks lakey.) Giving an explanation is deference to my husband's strong preference to give an explanation. While we walked tonight, we were discussing what happened to cousin and, going back to church and I used the "I'm keeping distance" without the explanation to see if he'd still mention that there needs to be an explanation. He did.
I explored the explanation giving with him and, I'm paraphrasing, he said "You have to give one because they expect it." (I felt like saying, "I expect them to stay out of my space," (cue the Stones) "You can't always get what you want." I didn't say (or sing!) that.)
I said, "Why meet that expectation?" He expounded a little and I got down to seeing it as a bit of a litmus test. (For this situation anyway.) So if you say, "I'm keeping my distance, my family is high risk," and they don't step back or get closer than they weren't just someone who was clueless and not maintaining distance, they're someone who doesn't care about your feelings or your health. Now, you can escalate the situation to something firmer.
My plan is to start with the limit and put the expectation after it, because, IMO, time is of the essence and I want the person to stop first and hear the explanation second. When we're walking, we've been able to cross the street and even do a quick jog to avoid people. I'm concerned that we'll be approached where we don't have a quick out and I want to be ready with some quick responses on which hubby and I have consensus. Because I'd like to cue the Meatloaf and sing, "Stop right there!" and leave it at that.