Is the issue about camping alone, being alone, or being separated?
My wife never liked being separated, so for my long TDY's, work trips, field projects, she either went to live with family, arranged to come along for at least part of the project, or visited. My biggest fear was that she would outlive me, I'd leave her alone. Didn't happen, I outlived her. So you need to understand how your wife feels about this, and decide whether you want to respect that.
Being alone yourself, only you know. I'm learning to live alone, have siblings that have always lived alone, but I visit my daughters, grandchildren, sisters, my wife's sister frequently, even if some of the trips are 2000-3000 miles.
I've tried camping alone (RVing actually) and so far it is not working so well, because it is something we alwats did together. Alone at home is easier, as I always have projects to stay busy. Camping alone has been more like solitude with enforced idleness. If you have a particular activity that kees you busy, that could be different, but just moving my house (RV) out to a campground and sitting thunking about the projects I ned to be doing at home, that has not worked.
Travel alone, that's a bit different, because I'm either with a group (even if they are strangers at the beginning) or it is a road trip and I'm busy driving.