Dogs are not wolves and wolf packs do not function as you describe.
There are 2 reasons that wolves form packs: to raise cubs and to hunt.
"Packs" are family units, they are made up of a breeding pair (the "alphas"), their juvenile or adult offspring, and the next generation of cubs. Alpha status is all about breeding rights. Alphas do not seek to control the actions of other pack members - this is a human construction. We see the necessity of controlling all of our dog's actions because they live in an artificial environment and many of their natural behaviors are undesirable to us - we therefore erroneously assume that "leaders" within the species attempt to do the same thing, when in reality it is all co-operative. No attempts are made to usurp the alphas because every wolf in the pack is related - adults and their children will not attempt to interbreed (remember, its all about breeding). When the children come of age many leave their pack to start a family of their own.
Wolf pack size is directly dependent on the size and abundance of game. Wolves in areas where the primary food source is large herbivores form large packs for successful hunting. Conversely, wolves in areas with plentiful small game, like rodents,
don't form packs at all. Their ecosystem cannot support it.
Dogs, unlike wolves (who are monogamous hunters) are considered non-monogamous scavengers. They do not form family groups to raise young or hunt game. Wild populations of feral dogs do form what are called "loose associational groups" but they only do so around human settlement to raid garbage dumps - food is an abundant resource, there is no competition or need to co-operate to tackle large game. They do not raise young in these groups, and the social structure is
far more fluid.
The dominance reduction exercises you describe (while they won't do any harm) have been proven in laboratory experiments to produce absolutely no change in behavior, especially behavior like SA.
A dog's fear of being left alone has nothing to do with how much of a leader you are, just as if you are afraid of heights, it has nothing to do with how much you respect your parents. Both are subjective feelings.
I do think that when a dog knows that all good things come from you (i.e. access to resources) and that all are conditional on good behavior it does produce excellent results. But things like eating first and always walking ahead of your dog are just smoke and mirrors.
I agree with LP:
- A bit more medical testing just to rule out all possibility of infection.
- Preventing the dog from being anywhere unsupervised when you are home and limit their access when you are not.
- Never punish the behavior, always reward heavily for successful toileting
- Leave lots of good things around for them to interact with when you do leave (i.e. daily diet frozen into kongs) and up the exercise when possible (leashed walks really aren't enough to tire a dog)
- videotape the behavior
- if other signs of SA become apparent, consult a certified behaviorist and do a bit of reading
http://www.dogwise.com/itemdetails.cfm?ID=DTB667
Good luck!