The fact that your Moms house is listed by an agent would prevent you from selling it without having your Mom still pay the commission.

I would guess that the likelihood is you will end up with far more tenants than just the father so if you do accept him you definitely need language in the lease to prevent that from happening. 

The less you know, the more risk you incur....why incur risk if it can be prevented?

Since you violated your own lease agreement by allowing them to have a pet you have placed yourself in a difficult legal position regarding preventing them from having additional dogs.

If these are removed, keep the base (which often cannot be seen from the ground) and perhaps seal around it to prevent roof leaks. 

The prospect of steady work may be enough to prevent being talked down to, but if not, fire them.

@Dave Van Horn and @Jerry W. we are looking at an opt-in (or out) system to prevent your being inundated.

Your loss would have to be pretty high, so in the case of A/C, you may want to try prevention and cage it instead.  

And tell them not to put the carpet back down without either a dedicated vapor barrier under the carpet (i.e. a piece of plastic sheeting if nothing else) or something to leave an air channel to prevent moisture from building up. 

My understanding (the way it was explained to me), is that the law was changed to prevent slumlords (not saying you are at all) from hiding behind a corporate name and PO Box.