Tenant shall be responsible for damages caused by his negligence and that of his family or invitees and guests.

I would suggest you send written notice to terminate the contract based upon their negligence for approving that repair without your consent.  

I would also acquire a copy of an up to date financial report for the property to see if they have been negligent with any of their rental payments. 

I'm saying they may be responsible if they were negligent and allowed the damage to happen.

Our house payment went up about $150 per month, but since our first deal was cash flowing at about $550 per month, we figured that this was negligible. 

If you didn't know what they were doing was unlawful then that is negligence on your part - that's not a defence.A professional should have indemnity insurance - that's the route I would try, to transfer liability to their insurer, that's the only scenario I can see where the PM doesn't escape by saying he was just following your instructions - in that case  he had a professional obligation not to.If he does not have indemnity insurance - well that is more negligence on your part for expecting  a professional service for someone who lacked professional credentials.

No sign of mold following November's abatement. 65% of their security deposit was used to cover a portion of this abatement because dryer negligence caused the issue.- In Dec 17 there are no visible sign of mold but a mother calls the property manager requesting an air quality test because her son has respiratory problems. - Dec 17 we do the test and it reveals mild elevation (500-1500 ppm) of either Penicillium (laundry room, 1 bedroom) or Cladosporium (bathroom).

However, if you go oafter the bank for their negligence in the process, you will walk away from the deal with money, the owner gets to keep her house, and the bank pays for their mistake. 

They don't realize that attorneys will sue you anyway, filing lawsuits against the LLC and you personally, under the theory that you are personally negligent as the property manager.

By owning it as an individual, you are opening up your personal assets to liability if something would happen at the property and you were sued for negligence.