Congratulations your American Pit Bull Terrier is acting like an American Pit Bull Terrier. Your responsible options are as follows: Learn a lot very quickly and start acting like a responsible APBT owner (which includes moving into Pit friendly housing). Rehome the dog with someone knowledgeable about the breed.
Take the dog to a shelter or get the dog humanly put to sleep (PTS) yourself- These are pretty well the same thing as the shelter isn't going to take the liability risk in rehoming the dog. Let's start with some breed history: While it's hotly debated how the APBT got it's start (be it bull baiting, as butcher's dogs, or as fighting dogs) there is no denying that the APBT is what it is today because of dog fights. The APBT was bred specifically to be a dog aggressive non human aggressive dog.
How was this accomplished? Breeding stock was tested in dog fights- Dogs that didn't "scratch" (crossing the line to go after the other dog) were not bred. Dogs that bit a human that handled them before (dogs were washed before fights and handled regularly outside pits), during (referees were in the pit up close to the dogs, owners were in the pits encouraging the dogs, and owners/ handlers had to hold dogs between rounds), or after fights (many a dog was picked up to fight another day or breed) were killed or never bred.
Over time this breeding selection resulted in a breed that was highly dog aggressive but human friendly to a fault with many top fighting dogs being picked up and stolen right out of the owner's yard. Because of this breeding program dog aggression (DA) is a genetic breed trait in the same way that herding is in a Border Collie's genetics. APBTs are not "trained to fight" just as a Collie doesn't need to be taught to herd (it just needs to be refined).
You can not love out or train out genetics (and thus it is not "all how they're raised") you can only manage it. A responsible APBT owner's rule of thumb is to never expect an APBT not to fight another dog. On the other side of the coin this breeding program also means human aggression (HA) is not a genetic trait and a dog that shows it is so far off the breed's temperament standard it needs to be PTS.
Bouncing off the topic of dog aggression it should be obvious APBTs have no reason to be at a dog park. Pups don't generally show animal aggression until their older but even if they are not DA you're setting your dog up for failure. Here's a good article that can go into more detail than I have space for here: http://www.pitbull-chat.com/showthread.p... Now for your specific case... All of these were preventable.
Every single one of them. Please don't think I'm trying to mean but these are the blunt facts based on your exact words: With the Chihuahua mix- Before getting the dog you and anyone you gave the dog to should have known about genetic dog aggression in the breed. Hopefully no one left the smaller dog alone with the APBT and hopefully his injuries were not sever.
We'll write this one off to be nice, we'll assume you didn't expect the dog to grow into dog aggressive traits. Then you left the dog in the care of someone with two small dogs knowing the dog had previously went after a small dog. On top of that you left an intact male with an in heat female.
Two males will fight or even kill one another over a female in heat. An unreceptive female in heat will attack a dog attempting to mount. You put your dog in a bad situation and there's no excuse for it.
Then you took the dog to a dog park. APBTs do not belong in dog parks period (as discussed above and linked to below). You took a known DA dog to a dog park.
You are at fault. You let a known DA dog off leash. With the media issues with APBTs today responsible owners keep even the best behaved dogs on leash.
Was your dog on leash you would not have been at fault, carrying pepper spay or another defense for off leash dogs would have been a great idea to boot. You again let a small dog near your DA APBT and still hadn't researched how to break up a dog fight. You're very lucky it only took 5 minutes.
Break sticks.
The American Pit Bull Terrier is dog-aggressive. This is the rule, not the exception. Your dog is acting in accordance with the breed standard's temperament.
Aggression toward other animals does not correlate with aggression toward people, though. Your sister-in-laws kids would have been perfectly safe. This dog needs to be leashed AT ALL TIMES.
I cannot stress this enough. Many pit bull owners buy into the "it's how you raise it" myth and don't know enough/anything about the breed and then things like this happen. The level of aggression this breed typically shows to other animals is the entire basis for their reputation--people incorrectly fear that a dog that attacks/kills other dogs will eventually turn on people.
Of course this isn't true. This dog needs to be leashed at all times, and perhaps muzzled while on walks. No more off-leash walks, ever, for any reason.
No more dog park. This typically cannot be simply socialized out of these dogs. He also needs extensive training and probably a whole hell of a lot more exercise than he's getting.
Get a doggy backpack for him to wear while out on walks. He should be worked up to a 6-8 mile walk or run (bikes help) every single day. This breed requires--REQUIRES--lots of exercise or they can become neurotic and hard to handle.
They also require extensive training to help curb the dog-aggression, if you can at all, it varies from dog to dog. This dog is probably not going to hurt anybody. However it might be best if he goes to a home more experienced with and equipped to handle this breed.
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