10 days of water will take up some room- Wet wipes for bathing, beer for hydration, pre-cooked then frozen meals mean you can get by with 2-3 gallons per person per day, if you use hand sanitizer and wash your hands sparingly.
Better to count on water purification instead, it is often intended for much more durable crap in the water. Bleach, iodine or a pump filter will render your water safe, just be consistent about cleaning the cap and spigot before you use them.
Wash up your dishes with soapy water and rinse as usual, a sterilizes spigot will remain so until someone else uses it. Viruses need you to multiply, they do not do so on their own, like bacteria.
You can make a routine that helps you remember what is clean and what is potentially not: phone in the clean hand, goes in a clean pocket, gets cleaned when this doesn't happen. Car keys in the other hand, other pocket, start the car and sanitize your hands before you touch anything else and the controls stay clean--no need to worry about them. Wipes are becoming available again, rubbing alcohol too, so set yourself up so these up where you use them and you will. When you have a protocol, being vigilant is simple and you can make room to relax and enjoy your trip. Being comfortable is the next most important thing after being safe.
Not sure where you're traveling, but regardless of what other people are doing, bring some masks and wear them around people, especially in close proximity and during conversation. Keep the inside clean (on your chin is not the place to do this) and count the outside as soiled. Surgical masks are effective, fairly inexpensive and disposable. Having a trash container with a lid can make the whole cleanliness process a little more simple.
As far as campground furniture, maybe avoid eating off of the seat of picnic benches or sitting on your hands while you eat. With sunshine and warm weather, these surfaces are unlikely to remain dangerous for much time. Even so, only touch things you know are clean once you've cleaned your hands and are eating. If you are not comfortable, bring some waxed paper to sit or eat on and dispose of it when you are finished.
You may not be able to stuff your car full of 10 days of clothes, so you can keep an outfit that you deal with the wider world in and others to relax in--Mr. Rogers style. If you have to use your car in the middle of that, throw a towel over the seat for your dirty clothes and fold it over on itself when you are done with it. Again, having a clear line in your mind about what is outside/inside or questionable/safe beforehand will keep you in a place that you can enjoy your trip. Have fun!