<human>: Provide a brief overview of the text.

Hello all! I've got two dogs, my boy dog is my most recent rescue, his back story involves abuse and kenneling for punishment ... Which brings me to my issue... 
He is PERFECT when I (or anyone) is home, goes to the door when he has to got potty, doesn't chew on things he's not supposed to, etc. 
But when I leave, he pees & poos in the house and chews on things he shouldn't. 
I live close to work, so I come home at lunch, I even built an elaborate "doggy potty": a 5' x 10' enclosed deck with fake grass and a doggy door for them both to use. He will use this sometimes. 
I do not want to kennel him, since he has BAD anxiety associated with a kennel and I am afraid he'll hurt himself. 
As a note: I ONLY use positive reinforcement training methods. Any suggestions you all may be able to offer will be appreciated! :)
<bot>: male dog acting out chewing & pooing in the house while I'm gone, have tried every possible thing I can come up with to remedy... Out of thoughts...