Tenant late on payments and has unauthorized pets

[Ben Kirchner]

A couple months into my tenant occupying my rental property, there have been issues.  This is my first rental property, and I'm learning from my mistakes of being too considerate to the tenant.  I'd like some advice for experienced investors on how to proceed with this one.

- First, I agreed to let the tenant pay the security deposit with broken up payments on agreed upon dates AFTER the move in.  She did not pay what was agreed upon on the dates we set out, and it took some hounding to get, but she finally ended up paying.  She had several excuses which I didn't really buy, but we were square in the end.

- I went to the property to do a 30 day walk thru.  I saw a dog in the house, which I was never told about.  I would require a $250 pet fee for this.  When I contacted her about it, she said she was just "dog sitting fort he weekend."  The tenant was there.  Instead, her Mom (who is an authorized tenant) and a man who I didn't know (unauthorized tenant) was there, with her kids.  An unauthorized tenant again would warrant a $250 fee.  She said he was just a weekend visitor.

- She was late on rent this month.  She ended up paying rent and the late fee on 5/10/17.  Again, this took some hounding.  She is not payed up.

- Today I went to the house to do another walk thru, fix something, and check on things.  This time she was not there, but her cousin and her cousins friend was there with her kids, along with the Mother again.  They let me in.  I saw dog food.  The dog was outside but later let in the house while I was there.  

My questions:

At this point, I certainly do not trust the tenant. She is paid up for May. I can't confirm if the other people at the house stay there or not. However, I think at the very least, she owes the $250 pet fee. My question is how would I enforce this? I see her giving me the run around about "just dog sitting." How can I enforce the pet fee, and are there ground for eviction based on this? Part of me says I need to be ready to push the button the eviction now, but I need solid reasoning, and also do not want to forfeit May's rent when she would end up occupying it for the rest of the month, regardless. Another part of me says wait until next month and file for an eviction if it's the 2nd of the month and she has not yet paid. That would at least start the process, and have her out with some time to start showing the house again in June.  What are my options?  Looking for how an experienced landlord would handle this situation.

Thank you