My sister lived on a beautiful spring-fed pond
and had this same problem constantly. She was very vocal but still had a hard time keeping people out. It was all neighborhood kids, and their parents were equally uncooperative.
DH and I live on a pretty, PRIVATE creek (property owners abutting the creek own it--my property line ends in the middle of the creek). It connects with another creek system and we had a huge problem with people walking through our yard to access the creek, or walking down the creek bank from another area, bringing their dogs to run around in private owner's yards, etc.
Our yard is almost an acre but we had a small 40 foot by 80 foot area fenced for our 2 dogs, near the house, and a good 20 feet from the back property line, 60 feet from the front property line, and 40 feet from the side property lines. People would be walking through our yards with their kids and /or dogs, our dogs would go crazy barking, and people would say dumb things like, "I just want to introduce my kids to your dogs"

confused3 ) or "Your dogs don't bite, do they?" We would answer with responses like, "Well, you're in my yard, and most dogs are protective of their territory." Geesh!
I'd even had people insist they had every right to walk their dog on my property and, while I've never called the cops on anybody, I've told a couple of the more obnoxious adults that if I ever see them on my property again, I will call the cops and get a trespass order. We even had a kid with a machete once, standing right outside the dog's pen, swinging the machete!
A few years ago, high winds from the hurricanes knocked a bunch of trees into the creek upstream from us, and that instantly cut the number of people walking through by 95%! It's been great. Lately there has been an increase in people walking through the creek, though, and I let my big dog out on the porch to bark ferociously at them.
I think fencing the front and sides of your property will work. I agree that it's really a shame you have to do that.