How will these two dogs live together peacefully?

Question
We have an eight year old mutt, large 80 lb. dog that we got from the humane society when she was 6 weeks old.  We just recently adopted a 1 year old 57 lb. australian shepherd mix dog from the humane society.  They are eating and drinking from separate containers in separate locations, and that is working out.  They go on walks together and they don't seem to have a problem with that.  They seem happy on walks together.  

The problem exists inside our home.  Our 8 year old dog is hiding from the other dog.  The 1 year old approaches, and the 8 year old either runs away or growls.  The 1 year old keeps trying to approach the 8 year old, but the 8 year old so far appears to not desire interaction with the 1 year old.  Unfortunately, they have been in two fights so far.  The 1 year old bit the nose of the 8 year old and made it bleed in their first fight.  In the second fight, my husband had to pull the two dogs apart because neither one would stop.  So, currently the one year old is spending time following me around the house and going wherever she wants inside, and the eight year old is spending time hiding under my husband's computer desk.  The 8 year old does not want to walk past the 1 year old, even to go outside.  I don't like this avoidance and aggression between the two dogs.  I have never experienced this problem with dogs before, and the 8 year old was not previously a growler or a fighter.  We know that the 1 year old was a stray prior to coming to the humane society.  However, the humane society had indicated that she got along well with other dogs and she was sharing with other dogs when we picked her out.  The two dogs met at the humane society outside and rode home in our vehicle together and seemed fine together.  So, how will these two girls be able to cohabitate peacefully?  We love dogs and we wanted to rescue another dog, but this current situation is stressing me out, which I know is not helping...but I don't know what to do or not do in this situation.  Should I just ignore them and let them work through it since they're mostly not physically fighting?  My husband thinks that over time they will work things out and get along just fine.  Is there anything I can do to speed up the process?

Answer
I don't know what you mean by "humane society."  Is this a NO KILL facility that takes unwanted or abused dogs?  Or is this a MUNICIPAL KILL shelter?  How a dog behaves in any shelter environment does not at all indicate how the dog will behave in a home environment.  You are obviously not sufficiently knowledgeable to do an accurate temperament test on your own and you can't (usually) trust the "experience" or anecdotal information of shelter workers, whether kill or no-kill shelters.  Additionally, allowing any new addition to freely roam your home is a mistake.  A new addition must be on restraint (house tab), long, lightweight training leash; and must be restricted (not allowed in bedrooms, etc.) until a true understanding of temperament and interaction is gained (which can take weeks, at least three to five.)  When introducing one dog to another in a two-dog home, opposite sex is usually best and BREED MIX is extremely important.  One must choose a breed with little or no predilection for dominance and independence (the Aussie IS NOT one of those.)  One must thoroughly understand the temperament of one's present dog and choose a dog that is most likely not to offer threat.  This is not as easy as it seems.

Your situation is difficult.  Two adult females who have fought as you describe will most likely fight on sight (at least the younger one appears to be the aggressor, perhaps responding to the older dog's obvious fear.)  Allowing them to 'just work it out' will result in a large veterinary bill (or worse).  This choice may have worked well if your older dog was not as "soft" in temperament.  She is obviously suffering enormously.  This is not humane.  Your older dog has preeminence in this situation.  She is terrified.  Return the younger dog.  Having said that, if it's a kill shelter you got the second dog from, you can't just return her.  If it's a bona fide no-kill facility or SPCA, she can safely return.

Your other option is to hire a credentialed animal behavior expert (NOT a dog trainer!)  You might be able to find one by contacting the veterinary college closest to you and ask for referral to a Ph.D. or DVM, but this expert MUST be able to come to your home (and multiple visits will most likely be required.)