I think you will probably have a hard time finding a dog trained in those " skills"

You mention having 2 dogs already and a cat(s)... but I am confused about this statement " Having another dog wouldn't work for us"

Most service dogs are a huge help to people with disabilities.. But everyone I know that has a service dog, That is there only dog. No matter how well trained a service dog is if they live a home with other dogs, they will want to play and enjoy the company of the other dogs so he/she wont always be able " to get between you and someone else" when you become angry.

Have you tried walking your current dogs and spending more time with them to build a good relationship with one or both ? Im sorry that your anger is scaring your child , of course that has to be a priority right now, no child should have to hide in a closet. I will say .. Any organization that trains and provide service animals will also interview you and will talk to your Pdoc because they need to know that the Dog will be cared for and safe.