Why does my Maltese shih tzu urinate over my miniature Australian shepherd, when the Australian shepherd is actually the dominant dog?
From the Editors of The Dog Daily
The urinating that you describe in called submissive wetting. Puppies will do this to demonstrate submission, but some adult dogs will also engage in the messy behavior. In adult dogs, it can also be a sign of fear and insecurity -- a sort of wetting-the-pants moment (without the pants) or the dog version of saying, "I'm sorry." Sensitive canines are prone to this.
Try to identify which stimulus is leading to the submissive urination. It sounds like your Australian shepherd could be asserting itself over your Maltese shih tzu, or even bullying it. Instead of yelling, "No!" or punishing the Maltese shih tzu, direct it toward more appropriate behaviors, such as reinforcing the basic "sit" command with both dogs. You may need to take them both to a training class with a professional to improve their relationship and help resolve the problem.
A veterinary visit may also be in order, as excessive urination can be a sign of certain health issues. It's best to rule out those before proceeding with other troubleshooting measures.