I don't know about your area but here a good farrier is really hard to find. If this one is good (with the horse's feet) I'd try to work it out with her, especially since you think your parents might have given her a mixed message. I think the barn rules sign is a great idea, as is calling the farrier to be very clear on the rules after speaking with your parents. Be calm (hard I know) but tell them that due to the elder dog you have, the birds and your horses you do not wish to have dogs loose on your property. It is your choice.
However I think to reduce your stress in this there is also room for you to move a bit. Your concerns for your elder dog can be handled simply by keeping her inside when you know the farrier is coming. She had an appointment right? Even if the farrier's dog was in the truck say the farrier needed a new tool or something the dog could accidentally get out of the truck and dust up with your dog. Prevention is worth the price! Also your older dog obviously stresses other dogs so even them being in the truck could be hard on her, let her stay in the house and have a nap, better all around. Do your chickens free range such that they would be in direct contact with this dog? Is there a run they can be in when your expecting her? Chickens can flap and squawk upsetting a horse someone is working under just as much as a loose dog so I always tried to have mine not there when I was using a farrier.
However I have to totally agree with you, nothing makes me so angry as irresponsible dog owners. I am a dog owner, I always make sure my dogs are welcome BEFORE they go somewhere, and if I'm out and about with one and have to go somewhere unexpected I'll call ahead and ask, or not go. I work in health care and you would not believe the folks that I work with that even think they can bring their dog into work if they are just stopping by! Filthy mutts they just ran in the park with mud all over them and no obedience training so they jump up and then jump on the chairs and lick everything. Gah! Gives all dog owners a bad name.
One more rant! Farriers. I got into barefoot trimming myself originally for the wrong reasons, I was sick of being stood up, waiting hours, being overcharged for shoddy work, not being able to get a hold of them to come back.... I started thinking I would just be barefoot when hubby was going in for surgery, we would not be riding much for months anyway, if at all. I used to trim and so got some tools and got back into it. I'll never go back. One chronically lame horse is now sound, the one that was 'lazy about picking up his feet' according to numerous farriers, and would always trip like that (he had fallen right down a few times) is miraculously cured. The rest of my horses are way healthier. Take a barefoot trimming clinic and do it yourself! Since I started again I have taken some training and it's not that hard to do.
