Siler - we know the reason that the dog is prone to UTI's - she is a female greyhound (rescue), and when they are preparing them to race, they give testosterone to the females to increase the size of their muscles. This can have the negative effect on the growth of their reproductive/urinary tract parts. In short, and because I don't know a better way to say it, the medicine makes her pee-hole stay closed after she's done peeing so that bacteria cannot get in.
I called the vet to ask about the chickens drinking pee (and dog being on meds), and they said everything is fine and it is safe for them and safe for us to eat their eggs - though I do hope it stops just because it's gross!
And buglit, I will try to catch a video of this, and if I do I will certainly post a link to it here!