Some good advice from alot of good peeps.. The title of the post say enough for me not to read the opening statement.
American PIT Bull Terrier ~ is revered worldwide as the ultimate [fighting] dog, thus its origins which EVERYONE is familiar enough to know they FIGHT.
You adopted a "Pit Bull" or what do they call em in shelters now: "pitties"? To soften the term.. no doubt. They really have no clue on dog origin or how to adopt these dogs out for the most part. I started as a vet tech for the SPCA by the way. Soon given the assignment of isolation dogs and dog/partner paring because I was tired of seeing people put down dogs they wanted but didn't need and adopting more dogs in the same manner. Come in put down her
APBT who was 7 and fine but no: "she was old and cripple" .. NO she was killing every dog she could. Then the lady sobs and sobs and BAM! she asks can I look at your small dogs do you have jack russells ..

ARRRGGHH!!!!!
Begging the question: should you put your dog down or can DA be curbed. ...
(I did read your opening post by the way)
Im a firm believer in understanding origin to understand YOUR problem, because its not the dog. The dog is a dog. You don't expect a wolf to be anything but a wolf do you? Do you expect a fox to be anything less than a fox? How about dogs? Do you expect them to be any less than a dog?
Don't assume anything less than two dogs of the same sex are gonna get in spats and if you do not assume alpha one of your dogs will. STEP UP and handle your dogs. If two adult dogs of opposite sex are suddenly put together they are just as likely to fight. The best fighting dogs ever were female. Don't piss a bitch off!

ANYway..
its real simple. All those wanna be dog trainers out there are screwing people up worse than the dogs which makes it even worse for people and the dogs
Richard F. Stratton ................. Get a book any book, and begin to understand the mentality of your dog, not your opinion of it nor the shelters nor the medias but the source of documentation of the breed collaborated for bulldog students like ourselves. Even more so GREAT for educating the PUBLIC not to go waving them in air but for sure keep the knowledge and promote people to search for the answers to their questions by diving in the book themselves.
If you have any confidence in yourself then all the training tips you need are here on GPB. I wouldnt pay any trainer: in which you walk in first day and leave your dog, in which couldn't take a problem dog or my dog and show me a change in behavior right then just something small that I couldnt do. inwhich has no breed knowledge of history or purpose. At most you need someone to show you how to break your dogs up.
get a pill bottle put some change in it, when they start that crap throw it at em or at the ground between em and let out a good gutteral AHT (AT) they'll stop usually and you then say "BAD DOG" I dont use bad dog very often but thats one time I DO. Then if they test you or tempt or taunt each other in any way ... AHT >> IN THE CRATE.. they will go. BIGGEST thing is DON'T panic. Then your dogs are fighting because your scared and they're protecting you. Relax.
People don't adopt teenagers into a home of teenagers without expecting quarrels, so whats the similarities here?
Trying is preparing to fail~ Did you adopt an
APBT to save it and give it a stable home: because you obviously like em or you wouldnt have gotten one, or did you "want to try and save one cause he/she seemed so sweeet?" A good deal of ch pit dogs were very sweet and their owners loved them dearly and they were the nanny dog for them while they were at work or in the field. Don't expect a "pitbull" not to fight........
Get TWO crates..
make you a dog corner. Give them a solid chew toy in their crate. Start exercising them more and in doin so work on your training. Dogs are built to run and piss all day..
What do people expect of them? They can't read a multitude of signs, they don't have opposible thumbs, and they are a walking liability because accidents are from ignorance which is simply a lack of knowing; which does not hold up in court.
IF the "pitbull" is not for you then ALL OF THE BREEDS that are considered PIT BULL type and are down from or cousins to such should also be taken off your list. If you can't handle DA and are afraid and don't want to change your views then you probably should just take it back to the shelter.
How ever, if you want to fight for the breed and keep your dog... Do the responsible thing even if you have to crate and rotate. Don't put two dogs of the same sex in the house and expect no fights or spats; don't adopt an adult dog to put in the home with an adult dog and expect no spats.. being relaxed around each other will be the best treatment for them. Go out in the yard and give them each a ball and keep the fetch game going. Walk em down to the water if you have any if not go somewhere that does. A tired dog is a happy dog. Don't tolerate DA and use a bean bag or a pill bottle to catch it in moment or before accompanied with that AHT, if it can be curbed it will be if it can't then CRATE and ROTATE or forget about bulldog breeds all together. IF it seemed like I repeated myself its because some things need to be reiterated.
Good luck and best wishes............