With that said I know it could be a huge mistake to let them stay but if they evict them I'm going to have to do a good bit of painting and clean up and possibly buy appliances.Also wondering if they will trash the house.

If the matter were simply a clogged toilet, the common sense response would be to clean-up the mess (maybe put a sign on the toilet) and call either us or the plumber in the morning.  

If they are German roaches, a few days after treatment, you have to go in and clean up the dead bugs.  

Or are you the owner responsible for the clean up?

That way if I have a vacancy and need  to do clean up, maintenance or improvements I have the entire Spring to find new tenants.

In your case, I would justify the intra-lease charge by pointing to the impaired usage of the property for the other tenants and the pet addendum terms calling for immediate cleanup of animal waste.  

I had it happen 2 other times as we used to do trashouts and cleanups in a company I used to own.    

They have no time to clean up and I am not asking for private areas; I am asking to see the two most commonly dirty places that untidy people have in their home.  

If they're Section 8, it's usually 90.Then, just get them out, do whatever clean up, painting etc., you need to do, and get new tenants in there who think it's a great deal at top market rate.Because it sounds like these guys are a pain, and honestly, whenever you inherit tenants, it's usually difficult.  

Just be SURE to seal the whole sucker in grout sealer (tile & all) so it is an easy cleanup between tenants.