I did not mean to imply that you are mistreating the dog here, I don't believe it to be true for an instant from any of the things you've posted. If I were in your shoes, you can bet me and my dog would not be on "speaking" terms for at least the rest of the day (I would have to shut them in the crate or the back porch except to go outside to potty, otherwise I'm afraid my patience would be overwhelmed by my frustration and anger) and my dogs would be avoiding me like the plague because they think I'm awfully scary when I'm upset whether I even look at them or not.
Personally, I do not think a muzzle will be a very effective solution. Dogs are very good at getting out of them, even when properly fitted (although a basket muzzle is often harder for them to get off and does not carry a great risk for overheating) and as anyone who works with aggressive dogs will tell you, a muzzle does not prevent a bite it just makes it a little harder. As to the training issues you are currently having with her, I'm sure it is just the stress from the new pups. Any major changes to the family structure are going to result in a backslide of manners and training. Every time we've ever brought home a new dog or foster dog my current dogs have had some sort of training issues (usually minor) and when we brought our first baby home from the hospital my extremely well trained 10 year old dog regressed to the point of pooping in the house. And even the best trained dogs will kill chickens given the chance. I don't think that this tragedy had anything to do with you being "negligent" in training your dog. It's just one of those unfortunate things that can happen when we keep both predator and prey.