You need to have an honest conversation with yourself about why you're doing this. A couple of possible answers are:
1. An additional income stream - in this case, you will need to work on optimizing your profit. You will need to define your process. What is a deal-breaker? Do you serve notice at 1 unauthorized animal? Two? Four? Or when you can smell them outside the front door? When do you serve pay or quit notice? One week late? One month? Do you serve notice immediately if you don't hear from the tenant before the due date, but allow a payment plan if they ask you before the rent is due? You need to figure out the rules, write them down and then follow them.
2. A charity - if you're losing sleep over enforcing simple rules, then this is not the right business for you. You will need to figure out your exit strategy - either sell the properties or donate them to a housing-related charity that is more prepared to provide this type of help.
An obvious takeaway is that you cannot care more about someone's ability to keep a roof over their head than they themselves care.