Sweet, loving and obedient may mean that she's submissive which is a symptom of an emotional problem for dogs and an indication that she would be difficult if not impossible to house train. Does she roll onto her back when she sees you paying attention to her? That was the more obvious symptom that clued our vet in to calling her behavior submissive. This dog also seemed too willing to please. She seemed to accept all of us as being alpha. She easily cowered. She wasn't obedience trained and she would cower rather than come running when we called her.
My mother took her and she worked out well in her home. She didn't even have accidents and always peed and pooped outside. The main difference was in the activity level in the house. I had a school age daughter who was rambunctious and unpredictable. The dog was home alone in a crate during the day.
Your dog doesn't sound submissive but the words sweet, loving and obedient rang a bell for me.
As for the urine stains. I had my carpet professionally cleaned multiple times and treated with an enzyme. Our next dog peed and pooped in that same spot. Even tho he was house trained in the previous home he goes to and uses this spot often. Sometimes immediately after being outside and peeing there. He comes in to poop here.
We had a doggie door in the previous house and none here. It's not possible to put one in. Our dog may be reacting to not being able to go in and out on his own as well as the smell that only he can smell left from the previous dog. Other than the inside pooping issues he's a really loveable dog who does will with grandchildren.
Your husband probably sleeps during the day and she may be doing her business in an out of way spot(s) or those that you find and don't know when or how they got there may have been deposited during the day.
Your dog may be smelling something that is on the floor below the carpet that you don't now about. He may also have issues, not as serious as submissive issues, from his previous home that he's acting out in yours.
I think your plan to take him out every couple of yours, as you would with a puppy might help. However, it sounds like she is house trained since she does go when she's outside. And crating her when no one's about will help. Other than that, I don't have any suggestions. Our dog is quite old and I'm not trying again with another dog.