I say this all the time: in my experience most people easily misjudge which dog of theirs is 'dominant'; it is so easy to do! This is why I so very strongly advise to NOT use methods of training or base any assumptions on behaviour on very outdated theories of dominance and submission and pack structure in dogs. Many people take exactly the worst approach to managing problems with their dogs by basing it on what they perceive to be the dominance/pack structure reasons for behaviour -- and most often IMHO they are wrong.
Read Jean DOnaldson's Culture Clash, many of Ian Dunbar's writings, and Patricia McConnell's The Other End of the Leash for example and you will realise how subtle dog and all canid relationships are. Pack leader animals almost never, ever, ever are aggressive or use any form of physical control. Indeed the leader is most likely to be the lowest key, most benign and gentle dog in the group that regularly allows toys to be taken from him/her by other dogs and so forth. A big problem with how people understand and interpret dominance theories (such as they are) is that 'dominance' has all sorts of emotional meanings in human language and it does NOT carry these same contexts and meanings for dogs, at all. We hear dominance and think: bossy, controlling, aggressive, pushy, misbehaving. For dogs, true 'dominance' simply means benign leadership 99% of the time. So if you peg the 'misbehaving' dog as the dominant dog you are almost always going to be... wrong! :lol:
Unfortunately some very old and poor standard research on captive wolves, long since disproven, forms the basis of much of what passes for dog training these days, based around 'corrections', physical handling of the dog, and these ridiculous assumptions about dominance, pack leaders in the house and so on. I have no doubt there's a correlation between this method of training -- very popular in the past 20-30 year and especially the past 5 years with the ris and rise of Cesar Milan and similar TV trainers, Dog Borstal etc -- and the very significant rise in aggressive dogs and massive increase in the number of dog bites medically treated even though the total dog population per capita has only slightly increased -- by about 2% in one recently studied 9 year period. Over 10 years from the mid 80s to the mid 90s medically attended dog bites rose by 36% in the US. In Britain, the number of medically treated attacks has risen 47% in the past 5 years.
Also it seems there isn't just ONE leader but often different leaders in different contexts. That also makes it hard to guess which dog at home is the leader and supposedly 'dominant'. In my house Leo is the leader of the group overall -- but no one ever guesses this because he is the sweetest, gentlest dog imaginable. Everyone guesses Jaspar but Jaspar is actually very submissive -- he is the one who will roll on his back when he meets many other dogs. Leo never does this. But Leo often takes cues from Jaspar in certain contexts, such as play. It is a very, very interesting area but it is always IMHO best to base training and management decisions on positive, rewards based approaches that shape and prompt desired behaviours.
Also: setting up dogs so that they behave as we wish -- eg preventing the problems in the first place by not feeding in proximity, managing treats, preventing flashpoints -- is definitely the best approach. We after all confine dogs down into tiny false territories which alters natural behaviours anyway so it's our job to make that work well for everyone, us and the dogs.