Laura,
I'm sorry this happened but you have got to know, this is what territorial dogs do. I know from experience because I went through this about five years ago.
First, if you really want to add another dog, you need to do some internet surfing on introducing dogs into your home. It's always on neutral ground or it can get really ugly...like it did for you, Cherry and Max. Secondly, your dogs were establishing hierarchy. I don't know who attached who but I bet it was Max attacking Cherry. That was his home and he was estblishing who was boss. Thirdly, if you can't handle what happened, I can pretty much guarantee you there will be no addition to your household.
I sent a Charpei mix back because of the same reaction from my dog. Then I got smart and did a lot of research on dog behavior and talked to people at work regarding the subject. About five years ago we added Sophie, same mix as Hillary and there was another bad reaction...but, because I did my research and faced my fears, we have been able to make it work. It was not easy. As a matter of fact, it took about a year not to have any scrapping going on.
Not all dogs are territorial by nature. You can pretty much bet two Labs or two Goldens are going to hit it off immediately but there are territorial breeds or just territorial dogs. Max might not mind being an "only" dog.
My dogs now recognize me as the alpha but it was not easy until I learned more about dog behavior and put what I learned into practice, which was difficult for me because I wanted to humanize them as well. Bit like Carola said, dogs are not human and have their own set of behaviors. When you learn what they are, it will be a much easier transition.
I know this has been extremely difficult for you and to tell you the truth, if it wasn't for my husband helping me out during the dog fighting, I would have given up myself. Good luck on whatever you decide.