dogs

I am not really a dog person- but we have two big black dogs, mildly lab looking. One is a lab/blue heeler mix we know, the other was dumped on our road so we have no clue. The heeler is the older dominant dog, and she gets real growly when people (esp. men) come to our house. Then she gets to know them and is fine. BUT
Today our neighbor up the hill came by, we don't know him well (we both have around 20 acres - we're country folk). He said our dogs have been coming up to his place and one of them bit his dog, and her leg had to have the surgery! He SAID (and I believe him) his dog just hangs out next to him while he works, but our dogs came up (on his property) and were growly and biting his dog. *sigh* And this isn't the first time they have been up on his place and all threatening, but we thought they were staying home better.
So we offered to pay the bill (his dog is going to be ok, thank God), and we put our dogs in the kennel. I hate thinking of them locked in a cage with 20 acres at their disposal, but they can't be agressive to other people/dogs - esp off our property! We have considered getting the "radio collar" fence things, it transmits a signal and the dog gets zapped if they go out of range. But the range is small - like the size of a town yard. Wish we could get something the size of an acre or two. My husband is completely opposed to a fence (traditional) and to have any sizable area fenced is a big pain anyway. Wish this never happened, but now I wonder if we should have the one dog put down, or try to give her away. I think she would be ok in a fenced yard. So depressing