OP, I am really really sorry to hear this. Unfortunately your brother is a hardcore terrier man, and therefore he will genuinely see nothing wrong at all in his dog killing cats, rats or other animals. In fact, he will see this as something to be proud of in that it proves his dog has a good track record in killing. He will almost certainly be using the terrier to dig or be set on other things and will know people who are involved in dog fighting too, as well as other illegal activities which I certainly won't go into detail about here.
I am aware the RSPCA prosecuted a greyhound owner last year whose dog attacked and killed a cat while out walking on a lead. The rspca argued that this was preventable and that therefore it was right to prosecute under the animal welfare act (this is one of the reasons why I am such an enthusiastic advocate of muzzles). However, given your brother's criminal associates, I'd suspect it's highly unlikely the neighbours (who owned the cat) would be willing to make an official complaint. If they are willing, then the rspca should be their first port of call. You could also talk to your local Council Dog Warden about the incident of the dog biting your DC, but again, you would need to be willing to go to court and the dog will almost certainly be PTS as a result.
I would also have a talk with your police force's Wildlife Liaison Officer (every force has one) who will be their resident expert on animal related crime. Even if they do not themselves take up this matter, they will contact with others who do. The RSPCA for instance does have a small unit of undercover inspectors who do some very good work on breaking up dog fighting/badger baiting rings - however this is extremely dangerous work and prosecutions are rare/expensive, and often the result of years of planning and work.
I think it's difficult for some people to understand, but there are large swathes of people who think that what your brother does is perfectly legitimate and is a cultural norm (both within the travelling community and outside it). I am sorry to have to say this, but in general the situation with travellers is not helped by the fact that police are often very reluctant to intervene so sites can be a black hole for animal issues ( I see a lot of this with greyhound/lurcher rescue, and in the way they treat their horses, but that's a whole other story).
I think you are very brave to stand up to your family and you are setting a great example to your DC. That takes real courage to go against something which is OK for everyone else. Please don't give in.