Hello and thank you for requesting me.
Shelter dogs often do this and this is usually due to lack of socialization when they were pups. They are usually given to shelters or new owners before they have had time to learn what bite inhibition is. This is why trainers will often tell you to yelp and walk away from the dog if it bites as this is what a litter mate would do. Sometimes this works but with dogs that have limited impulse control then the best thing is to teach them a command because they have a hard time remaining calm once they cross a certain threshold . It is equally important to play normal games with this type of dog and not do any roughhousing. Running and chasing with high pitched squeals and screeches get this type of dog all excited.
Keep in mind that children do run on impulse and though dogs normally run on instinct they too can have impulse control problems because they were not taught the proper way to deal with situations. In most cases you would teach the dog the command to leave it, and then direct him to a toy or bone that he can have. This teaches him that what he is doing at that particular time is not okay but he can do something else that is okay. The Leave it command can be used for many different things, from leaving that plate of food you just dropped on the floor alone to leaving another animal alone to not nipping or grabbing your body parts.
It is equally important to emphasize to the children safe dogs games to play as well. Keep in mind you have a dog that is part herding dog so it is in his nature to nip to keep a flock of sheep moving forward.
I am going to direct you to a site that goes over impulse control.
I am also directing you to a site for training. I would train daily in short sessions but train several times a day as your schedule allows as this shows the dog consistency.
Clicker training/positive method training/ print off
video’s to see how clicker training is done, scroll down to videos http://www.clickertrainusa.com/clicker-training-videos.htm
Also through daily training you will be helping with the SA as training in a positive manner boosts a dogs self esteem which helps them at being alone.