Landlord Issues- Advice Needed

[Fil M.]

So I bought a 3 family in NJ and have gut renovated all apartments and have had great luck thus far but have run into my real first issue. Here is the situation

I gutted one of the units (3 bedroom 1 bath) with a new kitchen, new plumbing, electric, bathroom and the apartment is immaculate. It is close to NYC transportation and I was amazed at how many people applied for the apartment (I had to take the add down). Long story short, I rented to a family with "two" kids, I say two because two turned into "four." Anyhow, I rented the apartment for October 1st. Everything was fine and then I see all of these people show up but they were paying rent and I did not say anything. Then the following week I see all these vases into the common hallway and back yard and told them they could not keep them there

Fast forward to today, I showed up to collect the rent and not only did she not have the rent, but she claims she did not have heat in the apartment for three months (which is rubbish bc I tested the heat back in October when it was still warm out and not only are the furnace that are two years old working, but i installed new thermostats). When I asked why didn't you call me, she said they got new phones and did not have my number. I told them they could have knocked on the first and third floors and they said they never saw them.

I started a new paragraph because I was interrupted in the middle of this rant by the owner of the house next store to mine who claims someone from my house was throwing cigarettes onto their rood (yes true indeed). I had also had a complaint when these tenants move in stating the people from the ins floor were throwing cigarettes on their property (note i did not have any issues with the other tenants until these people moved in). Long story short, the owner of the house next to mine stated the lady on the second floor gave them MY NUMBER and said no one in her apartment smoked. Funny how she had my number earlier today but not a couple of hours ago.

So my question is this, she is going to break the one year lease she signed in October, and is expecting her security deposit back; actually the remaining security deposit as she wants to use the "rent" for January out of her deposit. I told her no that it is not an option so my question is 1) Do I tell her to pay me the rent by the end of this week or else I will legally evict her or 2) Do I wait until the end of the month and hope she moves out on her own? The negatives with option 1 is that she can probably squeeze another 1-2 months due to our sluggish court system and she can destroy the apartment but I will eventually get her out. Option 2 leaves at the mercy of the tenant.

So to my experts, what would you do and why?