My dog and the neighbors dog!

[Clmcghie]

Hello my name is Cindy lee and I have 2 dogs. A female that is just over one year and a male that is 5 years old. They are both large dogs but generally have very good dispositions. I also own and train horses and like to take my dogs out with me. They are usually very good about coming when called and staying close to me.
I have raised both dogs from pups one from birth and they have been well socialized with kids and other dogs and animals of all kind. They are both respectful and do not show dominant traits such as growling or eating food that is set out but not for them. I have never hit them or scolded them and use positive reinforcement as a means of communication.
I live in a rural area at the end of road. My neighbor who lives up the hill has a large dog also. It is a German sheppard that is normally kept in a fenced in yard. When I moved to this neighborhood a year ago my big male dog and the neighbors dog had their first fight. My neighbour who also has horses and 2 little kids walked down to feed her horses with her dog off leash. Her dog charged in my yard at my dog who was obeying my command to stay.
We were able to break that fight up. Though skeptical we wanted to move forward and so we decided to take the 2 dogs out together on a group ride. I relize now that was not a good idea. I kept my horse to the rear and my dog stayed with me. My neighbour who was riding with her mom and another woman stayed to the front but their dog kept circling and attacking mine. I thought they would finally work things out on their own but things only got worse. Finally they had a really bad fight, both dogs hurt but my neighbors dog got the worst of it. I was alone my neighbour had ridden on ahead but i calmly managed to get the dogs broken up and on their way. I apologized to her and gave 250 dollar to go toward her 400 dollar vet bill. That was last year and since my neighbour and I have not talked much except for her telling me to keep my dogs away from hers. Until recently I have kept away from going past her house and riding on the trail just up from it. I went for my first ride out 3 weeks ago and unfortunately ran into my neighbour on the trail. Actually I was on the trail with my dogs and she was riding her bike on the road adjacent to it with about 20 feet in between. Her dog charged my younger dog and then my male dog and him went at it again (just the 2 of them) It was a terrible fight. I got badly bitten and had to go to the hospital. My neighbours dog was also badly wounded and had to go to the vet again. It was a crazy fight, my neighbour screaming and kicking and bashing with a dead cedar tree. I was trying to tell her she was making things worse but she persisted til she was spent. At that point my dog had locked onto the other dogs ear and would not let go. I tried to calm them but she kept screaming and so I finally start trying to separate them and got bitten by her dog every time my dog released. I was bitten 5 times and finally got them separated. She grabbed her dog and headed for her house. Luckily another neighbour came upon the seen and found me lying semi conscious on the trail. I punctured an artery and lost alot of blood. Luckily both my dogs stayed with me and my horse ( who I had let go of during the fight). My neighbour who found me asked my neighbour with the other dog to call an ambulance but the neighbour was so angry she declined. So after waiting close to a half hour with a turnkey on my arm still another neighbour came with my truck and rushed me 30 kms to the closest hospital. I was pretty bad off when I got there and had to spend 3 days on an IV drip.
I am an animal lover and I can understand what was happenning for my neighbour. She was panicked about her dog and also she was bitten once herself. I have been trying to find a solution because now her only solution is that I stay off the trail.
I might add that my neighbours dog does have a history of biting 2 people in our community. One was a boy the same age as my son who is 11 and they other a man on a dirt bike who was on the trail. I would like to find a peaceful solution and have been working with my dogs doing the "pushing" and tug of war. In my horse training methods I use alot of the same kind of thinking as natural dog training. It makes sense to me however my neighbour believes in the "alpha dog" philosophy. She isn't interested in socializing them and is instead is going to begin carrying bear spray.
I have decided to stay off of the trail for now as I don't wish to take any chances and because she has told me she would not communicate with me when she is going out. I would love to be able to take my dogs out on a ride with my horses. If you have any advise please let me know!