My puppy has diarrhea and won't potty train. What should I do?

Has Prudence been treated for intestinal worms? Those are very common in puppies, and would cause liquidy poops. If she hasn't been treated for it, give her a deworming treatment now and another in two weeks. I recommend Drontal or Panacur.

As for potty training her, patience is key. It can takes months to do. I can give you the method that has worked for me. Start by keeping your puppy on a regular feeding schedule, and taking away her food between meals. Take her out to potty first thing every morning, and once every 30 minutes to an hour. Always make sure she goes out after meals, first thing when she wakes up from a nap, last thing before bedtime at night, and right before you leave the house. Take her to the same spot each time to go potty. Her scent there will encourage her to go. Stay with her outside each time she goes to potty, at least until she is fully house trained. When she goes outside, praise her and give her a treat. You might want to consider crate training as part of her house training. It allows you to keep an eye on her for signs that she has to go potty, and will teach her to hold it until you put her outdoors. The crate needs to be big enough for her to stand up, turn around, and lie down, but it should not be big enough for her to go potty in.