The clue in your original post about the source of the problem is that the dog "broke loose" and went after the roo.
Dogs that are restrained -- particularly tied up -- with fast moving prey just out of reach are going to build frustration and drive to go after that prey. It's canine nature. We do this exact thing when training young protection dogs -- backtie them and elicit their prey drive by teasing with a bite sleeve or tug just out of reach.
I can tell you that if a full-grown pit bulldog gets hold of a rooster, and the rooster lives to crow about it, the dog did not intend to kill the bird. This was experimental and "playful" in nature. It could well have killed the bird, because chickens are awfully fragile, but if the dog had a well-considered lethal intent, the roo wouldn't have lasted a half second in her jaws. (YMMV next time.)
Your daughter needs to get with a good, effective, balanced obedience trainer who isn't afraid of pits. (It's scary how many new-age trainettes are afraid of big "tough" breeds, whether they admit it or not. Many will take your money anyway, and mince around twitching whenever the dog yawns while cooing about what a sweet baby he is to reassure themselves.) When the dog is taught to restrain herself, not be physically held back, she can begin to train her to be safe around poultry. You'll get a better all-around dog who you might like to have near you, and your daughter will honor her boyfriend's memory by doing the right thing for his dog.
You might consider taking the same lessons with your dachshund; little dogs deserve an education as well.
Predation towards poultry has nothing to do with aggression. It's predation. It's nothing personal.
Some dogs (breed irrelevant) cannot be trusted around poultry unsupervised, even after effective training. This will have to do with their degree of prey drive, how much it's directed towards feathered creatures, and their capacity for self-control.
I have a GSD with extremely high prey drive and virtually zero self-directed impulse control. None of her prey drive is directed towards poultry. Guineas have crash-landed in her run and spent unsupervised hours running, flapping, and shrieking under her nose. She doesn't appear to notice they are there. They are not, after all, tennis balls. Yes, this is an unusual animal, but shows how individuals can defy generalizations. This same dog is genuinely dangerous towards other dogs in her own pack -- she's a dimwitted social climber willing to try lethal force to get to the top. (Hence, she has a run. She gets free-range time every day, but is the only dog of mine ever confined in this way.) Absolutely harmless to strange dogs and all humans.
My English shepherds have poultry-guarding duties that they take very seriously. Predators fear the security crew. My youngest also has rooster-discipline duties, which require her to chase him and make him *think* he's gonna die, without ever actually touching him, and peel off when he's had enough. That's a tough thing to ask of a young keen stockdog, but she has not disappointed me.
None of my own dogs were raised with poultry. The youngest was a year old when I got the first chooks.
Yesterday my foster pup (6 months old) went missing. Found him inside the electronet with 117 five-week-old range broiler chicks. They were all perfectly content with one another -- he was eating poop and stealing mash. It took me and my older dogs about a month to break him of playfully chasing chickens (my layers free-range all day), but he learned well, and got free-range privileges himself. (He's accidentally run afoul of the broody a few times and gotten a good pinch, which supported the training very nicely, even though he was innocent of intent towards her babies.)
This can be done, with most dogs, with an outcome varying from complete success (dogs and chickens can range together unsupervised, and dogs will protect chickens from predators and theft) to a relaxed management protocol that requires that the dog be under command and have human eyeballs glued to her whenever she's in the same space as the chooks.
