We put a dog down about a year and a half ago because her issues in life were getting worse. I felt terrible because I had gotten her based solely on the reason that she was great with kids. Well, she was dumped off in 'the country' at a farm and we took her from that couple who were elderly and didn't really want her but felt stuck with her. We got her home and she was quite evidently an abandoned dog, she chewed everything in sight: power cords, boxes, tools, metal cans, plastic, paper, rigid foam insulation we put under her kennel to help her keep warmer and off the floor. Her worst habit was chasing trucks and bicyclist. She wouldn't hurt anyone, but it was so deep in her blood to chase trucks especially, that there was no stopping her. She was a nice dog in personality, friendly as a day is long, but we decided she wasn't worth the risk. What if she were to cause injury of a driver who was trying to avoid her? We weren't ready to take that on. Also, the bike riders were scared to death of her. Her method was to ambush from the shrubs we have along the road. She did get her paw run over by a FedEx driver once. BTW we refuse to tie a dog up. A dog should have room to stretch its legs.
The point is, even some great people dogs are not worth it if they cannot be trusted with those things we hold in a position of importance. If you cannot trust the dog with any other animals, then it is time to go. You might find someone who would want him and does not have other animals and would appreciate a dog who guards their property against unwanted animals, provided they could handle him on a leash if necessary. It sounds like he needs a great deal of obedience training if he is dragging people on a leash. If he is unstoppable even on a leash then you have more of a problem, you really cannot control him. The other alternative is to euthanize him. It is not cruel, in my book, to use a humane method of putting an animal down. It is painless and they just go to sleep. I witnessed our first dog go through it. And it just so happens that he was not tolerant of any other animals except dogs. We had him first so we didn't have any other animals until he was gone when he was almost 12. I have a St. Poodle now and the shock collar went on when I could not stop her from attacking the chicken wire and chasing any chickens that were out of their pen. She listens now and now some of the hens chase her.
I don't know what your son's disability is, but perhaps there is some other dog out there that would be even better for him and the whole family. I am sure the stress of what your present dog is doing is effecting him as well as the whole family.
Good luck in deciding, I know it isn't an easy one.