Welcome to YT.
I put my pee pads in one of those shallow, under the bed totes, and my guys use that.
However this still might not stop her sneaking off to other places. You praise her for going in the right places, but since you have never caught her going in the wrong places, you have not scolded her for doing that, so she doesn't know that it's wrong.
I don't allow mine the full run of the house, they are confined to the kitchen unless I am able to give them my undivided attention. That way if I catch them starting to go where they aren't supposed to, I can scold them and take then to the right place.
I will not allow them full run of the house until they consistently go to the door or the pee pad.
As for the dog eating cat poop, we had a dog in the past that did that so I put in a cat door to the utility room, and put the litter box in there. You could also put a gate across a doorway to where the litter box is, the cat can jump over it.
These little guys sure keep us on our toes. LOL
