My 6 week old mini schnauzer is sick. Could it be contagious to my kids?

Yes if infected. Dogs are a source of a number of illness that can be contagious to humans. Children in particular may be susceptible as their immune systems develop. Among the illnesses are GI infections which present with vomiting, diarrhea and abdominal discomfort.
DEPENDS ON THE CAUSE. Of the dog's illness.