I'm so sorry you're going through this; my heart breaks for you. When we adopted our greyhound, she was the first dog that both my husband and I had ever had. We were looking forward to being active greyhound community members; taking her to M&G’s, grey sitting for friends, and fostering for our group. But we can do none of those things now, because our girl has bitten other greyhounds in each of these situations.
As a result, our girl is an ‘only’ dog. Our cat is pretty savvy, and gives Bonnie her space. But when at an event with other dogs, we keep our girl muzzled. However, muzzles are only as good as the handler who's watching that they remain on. Muzzles will give one a false sense of security, as a determined pup is able to pry it off. They help in the short term, but because of their fallibility, and discomfort for the dog, they’re not a realistic permanent solution for keeping your dogs safe. Dogs are smart cookies, and will use a chain link fence, or a tree trunk, etc., to get it off. I can't tell you, how many muzzles I've seen come off at a greyhound run. You need only turn your back for a few seconds, and there it is, on the ground. I don’t know what else to say, other than I know how gut wrenching this problem is. I’m hoping someone can offer some hopeful behavioural advice. Sending you hugs.