If my child, or children, were frightened of dogs I would gently try to encourage them not to be. They often pick up fears from adults. It's quite significant that you said, "Children", and not, `"Child". There is something odd about more than one child in a family having the same irrational fear.
Children are scared of all sorts of things. I remember being scared of the vacuum cleaner (still am to a degree :)), of the spiky leaves on a tomato, and feathers, as a child. I outgrew those fears. I was scared and ran screaming on one occasion because a big dog came running towards me, barking, but it didn't put me off for life. A cat once bit me on the arm. However I like animals, all of them, and have had several pets.
Well trained dogs should be welcome in pubs, shops and restaurants; they lie down, they don't go around sniffing other people or scrounge food. If they do not behave they won't be allowed back. Simple.
It sounds as though the op has a phobia about dogs which is different to a fear and I sympathise with that but we can't restrict other people and their pets because of our phobias. I would rather not share space with a big spider and they are far more difficult to avoid! I do my best to deter them taking up residence in my home and try not to think about them.