OT but the snake on the beach thing would have had me walking on water away from it. I can apparently levitate through the air when I see a snake as I am deathly afraid of them. I have never, ever, in my life, tried to kick a snake. My flight instinct is very strong. Perhaps this lady doesn't have a flight instinct, but a fight instinct and when she sees a dog she perceives as attacking she goes into fight mode and kicks. Understandable...kinda.
I see this as no different than a very sever (insert deathly) allergy. If you are allergic to bees, you stay away from your local flower shops, large outdoor gardens and stick to more suburban areas where there is less chance of getting stung. If you are allergic to peanuts, you stay away from Thai places, candy factories, peanut farms and bakeries. Unless you are at work (which is a very different situation), if strong perfume triggers migraines, you avoid perfume counters, Bath and Body Works and any other really smelly place. You do not throw rocks at a business simply because their products can hurt you. It is the same with this lady. There are plenty of places to walk where there is a smaller chance of encountering dogs. No, walking to the grocery store and back isn't the same as walking around a wooded track but the exorcise is all the same. She can't have her cake and eat it too. She saw the dog coming down the path and only backed up a little, then acted aggressively and when called on her behavior acted like a small child about it. If she is so scared that her first reaction is to hit/kick etc, then she needs to not put herself in that position. I think the OP could have chosen her words differently and I would have said, "Did you just try and kick my dog?" but the lady bears 80% of the blame for not backing father away and kicking before seeing if the dog was out of control/aggressive.
I would also like to remind everyone that no where does it state that the dog was lunging. At most, the dog turned towards the lady and took a step. There is a very big difference between a lunge and a step. A lunge would mean that dog had jumped at the lady, the OPs arms were extended pulling and the dog had reached the end of it's leash. We see that no where in the description. If the dog had lunged, then the lady's reaction would be far more understandable. Excited walking (ie dancing or a small child hopping from one foot to another is vastly different than launching yourself at someone).