I have the same problem. The puppy apt wont make a difference and Ill tell you why. Jess is not a rescue but came from a show breeder so she became used to always having other dogs around. She is perfect when we are home
always goes on her pad. She even goes on her pad in the crate when we are out and she has a five foot long crate with a bathroom area. The problem is she gets excited or anxious and runs through it and drags It all over the crate. I have left her in a room with the crate open but she pooped right in front of the door. (shes only done this once) So we have tried all the separation stuff and tv on etc etc and it still doesn't work. She steps in it and squishes it around! So I have to take the bottom off the crate (it has a bottom thank goodness and hose it off.) I am trying to find a way she could poop and it drops into a bin of some sort. I thought of a litter type thing but Im afraid either A. she'd eat it or B. she kick that all over the crate. So I feel your pain..
looks like we are neighbors!