I see your problem, like you said "When we're not watching her every move" You HAVE to be supervising at all times. If you can not, crate her. At least til she's 100% potty trained.

If she likes newspaper, then maybe she'll like to be litterbox trained. They use newspaper pellets in the bottom of doggy litterboxes. I always thought if I ever got a small god that I'd litterbox train them along with the cats!