Check the document that property's state has regarding tenants' rights: in the state I invest in, it says that withholding rent for landlord disputes is illegal. You'll need to educate the tenant on the proper channels to go through to resolve the issue. I make sure my tenants have a link to that document for both of our protection. For example, if it's a maintenance issue and it hasn't been done or done to their satisfaction, I instruct them to send a certified letter and if it's not resolved within 3 days of the date of the letter, then they can hire their own maintenance tech and invoice me or the property manager for the expense. We also have to allow for reasonable amelioration to complaints before evicting on a lease violation.
If it involves an animal as yours does, get the local animal control involved (noise, dangerous, etc) to guide you through what the other tenant can do. But work with them through the pathways that are allowed, empowering them to know what they are, because sometimes tenants feel they only have rent withholding as a weapon. Animal control has solved my pet nuisance issues on numerous occasions because that has nothing to do with evictions, and they are subject to those regulations as an animal owner.
Your local Apartment Association will be invaluable as you work through these issues as well. Our state has a free support line for all landlords when we have questions, and they have referrals to attorneys and other providers like mediators. You can also give your tenants contact info for free tenant legal support with local organizations. You are in the right here, rent withholding is only legal in certain circumstances, and there are so many resources to guide through the dispute process.
Also, I really like the tenant empowerment approach of Mr. Landlord, Jeffrey Taylor, on how to run a rental business with boundaries the tenants can self-act inside of (similar to the 4-Hour Work Week philosophy of empowered delegation). It resonated with me because it's how I raise my kids and run my business, and made the connection that tenants can be easily managed using the same empowering tools that I enjoy as a tenant.
In a high-regulation are like you are in, having an eviction attorney to consult with on these issues is important, because it can be tricky. Having legal advice with the Apartment Association can no longer help is a good line item expense to have on your budget.
Hope this helps with some resources to go to as you research the best way to handle this!