MilaMae - I do feel for you and your son. It's a horrible thing for him to have to go through, and for you to watch.
However, I do think that your suggestion that dogs are only allowed in specific places so you can enjoy the countryside in peace is a bit strong. I also pay my taxes, and I live in the countryside, and that is mainly because I love to walk, with my well behaved dog, in said countryside, including beaches. I use it every day, not just when it is sunny. To ban me from everywhere would have just as big an infringement on my enjoyment of life as inconsiderate dog owners have on yours. Possibly bigger, because I am out for at least an hour, more usually 2, every single day of the year.
This is no way diminishes your son's experience, and if you did indeed choose a dog restricted beach then that owner should have had more respect-s/he was an idiot (or stronger) to let his/her dog run free on a restricted beach. I don't mind some beaches being off limits, but please don't ban me from going anywhere at all.