You have a good potential case. Unless certain very limited exceptions are met, the landlord cannot enforce this and it violates federal law.

The biggest problem is you have waited a long time. You'd need good reason for your delay. Yes, you can file to get your dog back but as noted...

Lying to the court is a terrible idea.

This is complex and you need an attorney.

If this is the entirety of the situation, it is not worth reporting.

Report this to management, animal control, and the police each time. In writing. You could also have an attorney do a cease and desist letter.

Call the police immediately and file a report.

Consult with an Animal Attorney then do a small claims case for the amount if the stud fee/cost of a puppy.

Many of the online services are fraudulent. If your dog is an ESA, and you want to stay, you need to consult with an Animal Attorney who can...

File again and let the court know what has not been followed.