Removing a subletter

[Tyler Green]

I have an inherited tenant that fell behind on rent and I made the mistake of allowing her to make payments and catch up. To speed up the process she decided to advertise for a sublet to split the rent. She said this would be short term. The subletter has a child that they needed to enroll in school so I provided a note to the school acknowledging that they were subletting at this address but I did not add them to the lease.

Now my tenant wants to kick her out and is asking me if "we" have to give her a 30 day notice. 

After acknowledging that I should not have allowed her to fall behind and then I should not have allowed the subletter, any insight on how to remove a subletter. The original tenant has been working really hard and is almost caught up and she wants to stay.