Wow, this thread has come a long way and you've gotten some great advice!
I want to confirm you can have both, a dog that's a good family pet and a good working dog. My dogs sleep in the house, next to my bed. Last night my dog woke me up at 4:00am. At this hour it usually means the dog has to go out and pee, but the dog wouldn't go out. You need to learn to read your dogs (as well as them learning the things you train them to do). I know my dog would not wake me in the night for no reason. I know my dog would not refuse to go out given the opportunity. I need to know/learn what my dog is telling me, and it takes a minute to process at 4:00am sometimes, but what my dog is really telling me is that the coyotes are here. My dog is working even in the middle of the night while sleeping next to my bed. She alerted me the coyotes were here. I can go turn on outside lights and look at windows and check the chickens. Dogs are smart. Do not ignore them when they are trying to tell you something.
You also asked about training. The basic training is the same. The techniques are the same. You are training your dog to "ignore" things that are exciting. This could be running kids, cars, the trash, the food on your dinner table, and the CHICKENS. You are teaching calming behaviors and ignoring stimulus. Encourage being calm throughout the day, even when there is no exciting stimulus. Its easier for dogs to learn to be calm when there's nothing around to excite them, then you can slowly start adding distractions for them to ignore. Lot's of sitting and staying and laying down and petting and treats and talking in a soothing voice. If you are calm your dog will read this and understand that there's nothing to be worked up about. We did lots of sitting next to the chicken coop (chickens locked behind a fence, could be seen and heard by the dog), and being calm. I'd just sit there in the lounge chair daily and make my dog sit next to me and pet her and tell her how good she was. Whenever she would get up/get excited by the chickens I'd make her come back to me and sit next to me (but you need to teach come and sit first, without chickens around). Once she could be calm around chickens I moved to giving her a job to do and pairing it with a command. Now in the morning instead of just asking the dog if she wants to "go out" I ask her if she wants to "check the chickens" and together we go straight from the front door to the chicken coop. She now associates this phrase with going to the coop and I can tell her to do it and she will go to the coop without me. When we are at the coop together we "check the chickens" and we walk a full lap around the coop and run. This is all very exciting for my dog and she is automatically rewarded by eating chicken food and chicken poop that has come through the fence (dogs love it, I can't stop it, it reinforces the positive behavior of circling the coop so I just go with it). After doing all this with me repeatedly, she knows to go "check the chickens" on her own, I can just send her out the front door and she runs out and does a lap around the coop. She will sound the alarm if anything is amiss and I don't even have to go outside.
I hope some of this helps and you can see the training steps and transitions. You'll get there and it will be rewarding for both you, the chickens, and the dog! Good luck.