One more thought. It may not apply to you at all, but it is worth mentioning if others are having similar issues with their dog.
Upon studying, I read many times that if a dog was punished at one point for pottying inside the house, then they may sneak off and pee/poop when owner isn't looking.
A dog, for example, quickly learned that he will be punished/yelled at/swatted/time out/etc for going potty, (generally inside when they are young or new to a household) so they begin to do it "secretly" hoping they won't get in trouble. The owner may mean well in the original training, but the dog never got the message that pottying outside
is to be rewarded.
Rather, the dog simply learned that pottying in general gets him in trouble-- so he best do it on the sly inside when owners aren't noticing.
Again, I am not at all suggesting this happened to your dog. Many dogs are rescues and this stuff happens when they are pups, way before our dogs get to our homes.
Potty training again with very frequent trips outside, ultra delicious food rewards and high praise for outdoor success may help you guys in the long run.