Pugs

Tilly and I have a Pug. We did a lot of inquiring ( we thought) before we purchased her 3 years ago. We paid out the wang-wang for her. She is a lovely little companion to Tilly while I am gone. She like me, but is crazy about Tilly. She seems pretty smart, but is undoubtedly the most stubborn canine we have ever owned. We diligently house broke this dog as a pup, but she still doesn't get it.
She will go out doors, wander the yard, bark at the neighbor's beagle, and anyone who walks within a half-mile of our yard. When she finally decides to do her "business" she turns in a full circle in the same spot not once, but many times, (I have actually counted up to 16 circles) then finally does her thing.
The only thing is, she will come back in the house and 15 minutes later, poop on the floor. She has completely ruined out living room carpeting, and has a favorite spot in the dining room. I think she does this out of spite. Is that possible or is she just too stupid to catch on that she is supposed to take care of all bodily functions OUTSIDE?
She is also a notorious shedder. We had Kees before and they shed a lot. But I honestly think that she tops them. She doesn't have a hair on her body longer than an inch to an inch-and-a-half, and she sheds like a cat. We have tried switching food, grooming (actually overgrooming) and still she sheds. I hate the hair. It's brittle and gets in the weave of a sweater or even my slacks and shirts, and is hell to get out.
All in all, I would give her to the first band of gypsies that would go by,(I threatened my kids with the same treatment when they were still home) but Tilly says NO! Tilly did concede to running an ad to see if someone was interested in buying this dog, but when someone expressed interest, she changed her mind. "She wanted to cage her all day while she is at work. Pansy has never be caged, she would be traumatized." So, here we are, still cleaning up after a 3 year old dog, brushing the hair from everything, and still having her lay close and snore in the way only a loving, content Pug can do. Anyone got any suggestions?
JE