i am having the same problem. my puppy pees in his litter box but when it comes to pooing, it is different place every day and i have to watch him like a hawk. one thing i do notice, when his litter box has pee and is kind of wet, he will not pee in it for a second time so i have to replace it each time and i guess same goes for the poo. he will only use his litter box when its clean and fresh minus a little old pee smell
and i bring him for walks before and after he eats to the doggie park. he had poo and pee outside before but it is not guaranteed. he will do it when he wants but usually, he will only want to play when outside and i tried to stay as long as 45 mins..he doesn't do anything but as soon as we come back, he poos.