If your HOA prohibits dogs for short-term rentals at your townhouse complex, but an owner continues to allow renters with dogs, there are several steps you can take. First, document any instances of violations, including dates and details. Then, formally report these violations to the HOA board, providing your documentation. The HOA should enforce its rules and may impose fines or other penalties on the violating owner.
If the HOA fails to act, you may need to explore further legal options to ensure compliance with the HOA's regulations. My guess is the HOA will give you the relief you seek if you can properly document the violation.