New dog in house

Question
Hello, we have had a dog for about two years and just brought another one home.  The dog we have had is a lab/Rhodesian ridge back/Shar Pei.  We just brought home a new 13 month old boxer and the boxer is doing great wanting to play and such but our other dog is incredibly territorial.  I have heard that it is good to let them kind of fight it out when they get into tiffs so they can figure out who the alpha dog is.  Is this correct?  Both dogs are females and our dog has had aggression towards other dogs before but nothing she couldn't figure out.  When she was a pup she was abused and neglected.  What steps can we take to get them to at least be at peace with each other?  I read in one of your other answers that walks are the key so we are going to start that right away!  Thanks for your time!

Answer
Do NOT LET THEM FIGHT IT OUT!!!!!

Your present dog is not a good candidate for a "brother", let alone a "sister".  Your present dog was most likely not socialized to other dogs as a puppy and has issues (perhaps fear related, can't tell that from here.)  (I don't know how you get a three way mix...lab/ridgeback/shar pei?) You have two independent, strong and stubborn breeds (one mix.)  They should have been introduced OUTSIDE OFF YOUR PROPERTY, on leash, walked parallel and then allowed to interact, BEFORE bringing the Boxer indoors.  Too late.  Walking dogs parallel to one another can assist them in developing a tolerance for one another but it will NOT fix an escalating aggression problem between them (especially two females!)  You must closely observe this "fighting it out" == watch body language, observe which dog is backing off, do NOT ALLOW blood letting.  Be VERY VERY CAREFUL how you interfere; do NOT reward and do NOT punish, this takes some degree of diplomacy.  If you are able to determine which dog is more dominant (which I have my doubts you will be able to do), repost for instruction on how to promote that dog.  My suggestion is you bring in a certified applied animal behaviorist if you perceive this relationship is developing in a manner you cannot determine or facilitate.