Teach your children how to interact with dogs in public.
Often while in public, we will get asked frequently by children if they can pet the dogs we have with us. Sometimes they don't even ask, they just run up and do it. While we do bring dogs into public to work on socialization skills, it is important for children to understand and have knowledge of why they are out in public. We have dogs that come in with high anxiety, aggression, and that are reactive. Although, we don't bring these types of dogs into the public until we feel they are ready, a child running to a dog in public that is still in training, could trigger old memories the dog may have. We are always paying close attention to our training dogs so we can correct any bad behavior that may arise.
This also goes for service dogs. Service dogs are trained for the specific needs of their owner. Every time they go out into public with their owners, they are working. These type of dogs are best to leave alone completely. They need to concentrate on their job of protecting/ alerting/ watching out for their owner.
Always teach your children to ask the owner or handler before allowing them to pet the dog. Sometimes it is best for them not to and in some situations it is ok.