It is a Chihuahua's nature to be aggressive and stubborn and very difficult to train. A Chihuahua takes itself very seriously and expects you to take it seriously as well, when you do not it gets angry. When you take on a Chihuahua rescue dog not only do you have all of that going on, but now you have the added dimension of whatever damage the trauma has caused the and what you will need to do to get through that. It is a frustrating thing to train a Chihuahua and they do not adapt well to being mistreated so it will take time to get through to your new dog.
Before you can even hope to begin any of the basic household training that your Chihuahua will need you first need to get through the trauma it has been through and Chihuahuas do not react well to bad situations. All you can do is spend a lot of time with your dog and let it know that everything is okay and show it that it is safe and loved in its new home. Patience is the key to this.
Probably the most difficult thing you will have to do with your new Chihuahua rescue dog is refrain from punishing the dog at any point. Punishment to a Chihuahua is confusing and could trigger a biting reaction. Since you are dealing with a previously traumatized dog the chances are pretty good that the biting reaction is already in full effect and you will need to counteract that with love and affection. It will not always be easy but it can be done.
A Chihuahua that has been abused may or may not come to you housebroken. Chances are even if it was housebroken it will rebel against everyone by doing whatever it wants wherever it wants and that is never a good thing. You will need to try the standard methods for housebreaking at first but remember that housebreaking a Chihuahua under normal circumstances can take months so patience and understanding is very important.
Many people find it very cute when a Chihuahua defends its territory with barking and growling. While it is cute this behavior is also something that should be stopped immediately as it can develop into more aggressive behavior later in life.
In a Chihuahua rescue dog that instinct to violently protect itself and it's possessions may be very strong so you are going to need to exercise a lot of patience and show the dog that it is loved and safe where it is. It will take time but more than likely you will have to deal with it.
You are not alone in your raising of a Chihuahua rescue dog. Don't forget that your vet is a great resource should you ever have any questions or needs of any kind. Also try and get in touch with a local Chihuahua breeder and see if they will offer any advice.
When you are trying to raise a traumatized dog you will need all the advice you can get.