I don't have children myself but quite often see small children who appear to be petrified of dogs
Well at that age their developmental wiring teaches them to be frightened of anything and everything. It's nothing really to do with the parents and everything to do with genetics. Although unhelpful and anxious parents will make it worse. If you watch a child's development of fear of say strangers it follows quite a logical pattern - nonexistent at the start (no need as always with the mother therefore a stress response would be wholly negative) to developing at crawling age (stranger fear from removing from the mother - a stress response would increase chances of survival) to completely in overload (toddling age when often away from the mother - a stress response would almost certainly increase the chances of survival). I guess what I am saying is that it is unrealistic to expect children not to be frightened of dogs or anything at such ages - it's quite normal.
As to this specific dog - well it's from a breed that has been bred for a purpose rather unrealistic to expect it completely placidly in all circumstances. But most dogs will be more indicative of their owner than their breed but saying that I would not leave the kids alone with the animal no matter the owner or the breed.