It's important to not force yourself on others. "What you do in your privacy of your own pants is your business" is what one person here said, and that's basically it. As long as you're not making a scene or spreading offensive odors, do whatever you like. Walking around in a store in wet pants is going to make a scene. Walking around in a wet diaper on the other hand, hopefully will not.
Yeah, in your car I suppose is fine for the public, though cleaning the upholstery and keeping the car from getting smelly is something you'd want to think about? I'd suggest you try to embrace wetting your diaper rather than wetting your pants. No social problem, less mess, that's what they're designed for. If you want to wet in public view, diapers are the way to go, and will allow you to do it anytime, anywhere, without reservation or creating problems later that may limit your options.
If you want to be a bit more "exposed", there are some options for you that don't have to involve the public. I like to sit on my front porch and watch the traffic go by late at night, wearing only a diaper, tshirt, and socks. It's pretty dark on my porch at night and I can't clearly be seen from the street, so I can have that "fully exposed in public" feeling without bothering anyone.
That, and why make more work for yourself? I'd get less enjoyment out of my diapers if I was constantly having to clean things up or do more laundry. Isn't it easier to just come home, change your diaper, and head back out?