So the good news is, that I get my care at the VA and "South Dakota" where my new residence would be, does not currently have the program I am in. The closest with the program I'm in is in my home state (MN). However, I am planning on moving around outside of my home state as well. I just have to stay under 30 days. For South Dakota, you can stay one night and change your residency.
The way you described the bathroom and shower facilities is what I was referring to as "Unisex". I simply meant that there is no Gender Sign on the door. You enter from outside and have a single stall. That works for me and those are the kind I'm looking for.
The other thing I could do, to sort of avoid getting stuck in Minnesota is to do some virtual groups and maybe come in once a week. If I park in the Hudson WI area, it won't be more than a couple hours drive either way and I'll get my Travel Pay for that anyway.
I did notice some places are hiring in a work for campsite capacity. I'm totally on board with that, but one of the places I saw required a couple. It's only me and my Dogs and my Service Dog can't exactly do what part of the other role is.
Thank you for your feedback.