Cat problems in my rental

[Merrit Olson]

Sure could use some advice on this one.

I bought a rental and the lady living in it has four cats.

In her previous lease agreement, she agreed to having no animals, but obviously that did not happen.

Now I have also told her that the cats have got to go, but I believe she will just hide them from me since I have to give her 48 hours notice before I enter the premises. 

The only solution I could think of is to ask her to agree to a couple of random checks a month when she is not home. 

This troubles me, because I do not want to infringe upon her privacy. 

I could also just tell her I’m not going to renew her lease, but she does pay her rent on time and I don’t want to kick out a single mother with two small children in December in Montana. 
I really don’t think I can trust her since she has already broken the lease with the previous owner, and she did not have them out of the house by the first like she agreed to. 

She had been letting the cats poop in the basement, and there was a pile of cat poop 3 inches high over in this one corner.
On top of that, they run all around the neighborhood and cause more destruction. My 90 year old neighbor lady was begging me to have her get rid of the cats.

 Thank you in advance for all your help,