Should I allow this tenant to relocate to another of my properties, which neighbors her cousin, who is a terror?

[Lee Miles]

I have a current tenant who wants a bit more space than the unit she's in currently. She's interested in moving into a larger 1BR at another multifamily property of mine.

This tenant takes care of the unit she's in now, but she always pays late (sometimes incurring a late fee, sometimes within the 5 day grace period). She has a good job and shared custody of her two children, both of whom are well behaved. However, when I showed her the larger apartment, she mentioned that her cousin lives in the duplex beyond the alley behind my rental property. Upon hearing this, my heart sank...

See, my tenant's cousin (and potential new neighbor) is a low life. She does not work, she's often drunk and, and her children (aged 6-15) are an absolute terror. These children are out of control and they're the apparent ring-leaders for the other neighborhood kids. No good.

One of my workers rents the other side of the duplex "cousin" lives in, and they've called the police on this "cousin" and her children multiple times for noise disturbances, threats (from the mother and her boyfriend), and vandalization (the kids ripped my my workers vegetable garden and threw the veggies onto his porch!). This area isn't "the hood", but apparently this "cousin" person isn't on board with peaceful living. ;)

I'm afraid if I let my tenant relocate into this apartment, the cousin and her family will begin spending time in and around my property, making life harder for the other tenants in the triplex. I'm also concerned for the condition of my property as well as any liability I may have for someone getting hurt while on the property. 

Lastly, I don't want to engage "cousin", as I'm told she can be quite malicious. She's got nothing but time on her hands to cause me grief. I'd much rather steer clear of her so long as she's not bothering me. I certainly don't want to give her reason to be on my property! My tenant isn't aware of any of my knowledge of her cousin.

So, I've got a tenant who takes good care of her apartment - but pays late every month - wanting to move into a property which is basically next door to her close family, who are also the worst neighbors one would never ask for. I'm inclined to not rent this unit to her, but not sure what my legal responsibilities are. I'm okay with losing her as a tenant.

What is the best way to handle this situation?